Turbulence and holography (with D. Minic, Y. J. Ng, and C.-H. Tze)
arXiv:0806.0030 [hep-th]SPIRES Abstract:
We examine the interplay between recent advances in quantum gravity and the
problem of turbulence. In particular, we argue that in the gravitational
context the phenomenon of turbulence is intimately related to the properties
of spacetime foam. In this framework we discuss the relation of turbulence
and holography and the interpretation of the Kolmogorov scaling in the
quantum gravitational setting.
On the origin of time and the Universe (with M. Kavic, D. Minic, and C.-H. Tze)
arXiv:0804.3598 [hep-th]SPIRES Abstract:
We present a novel solution to the low entropy and arrow of time puzzles
of the initial state of the Universe. Our approach derives from the physics
of a specific generalization of Matrix theory put forth in earlier work as
the basis for a quantum theory of gravity. The particular dynamical state
space of this theory, the infinite dimensional analogue of the Fubini-Study
metric over a complex non-linear Grassmannian, has recently been studied by
Michor and Mumford. The geodesic distance between any two points on this
space is zero. Here we show that this mathematical result translates to a
description of a hot, zero entropy state and an arrow of time after the Big
Bang. This is modeled as a far from equilibrium, large fluctuation driven,
"freezing by heating" metastable ordered phase transition of a non-linear
dissipative dynamical system.
SQCD: A geometric aperçu (with J. Gray, A. Hanany, Y.-H. He, and N. Mekareeya)
JHEP, 0805, 099 (2008)arXiv:0803.4257 [hep-th]SPIRES Abstract:
We take new algebraic and geometric perspectives on the old subject of
SQCD. We count chiral gauge invariant operators using generating functions,
or Hilbert series, derived from the plethystic programme and the Molien-Weyl
formula. Using the character expansion technique, we also see how the
global symmetries are encoded in the generating functions. Equipped
with these methods and techniques of algorithmic algebraic geometry, we
obtain the character expansions for theories with arbitrary numbers of
colours and flavours. Moreover, computational algebraic geometry allows
us to systematically study the classical vacuum moduli space of SQCD and
investigate such structures as its irreducible components, degree and
syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau
cones over weighted projective varieties.
Entropy of near-extremal black holes in AdS5 (with V. Balasubramanian, J. de Boer, and J. Simón)
JHEP, 0805, 067 (2008)arXiv:0707.3601 [hep-th]SPIRES Abstract:
We construct the microstates of near-extremal black holes in AdS5×S5
as gases of defects distributed in heavy BPS operators in the dual SU(N)
Yang-Mills theory. These defects describe open strings on spherical
D3-branes in the S5, and we show that they dominate the entropy by
directly enumerating them and comparing the results with a partition sum
calculation. We display new decoupling limits in which the field theory of
the lightest open strings on the D-branes becomes dual to a near-horizon
region of the black hole geometry. In the single-charge black hole we find
evidence for an infrared duality between SU(N) Yang-Mills theories that
exchanges the rank of the gauge group with an R-charge. In the two-charge
case (where pairs of branes intersect on a line), the decoupled geometry
includes an AdS3 factor with a two-dimensional CFT dual. The degeneracy
in this CFT accounts for the black hole entropy. In the three-charge case
(where triples of branes intersect at a point), the decoupled geometry
contains an AdS2 factor. Below a certain critical mass, the two-charge
system displays solutions with naked timelike singularities even though
they do not violate a BPS bound. We suggest a string theoretic resolution
of these singularities.
Time and M-theory (with M. Kavic and D. Minic)
Int. J. Mod. Phys. A, 22, 3317 (2007)arXiv:0706.2252 [hep-th]SPIRES Abstract:
We review our recent proposal for a background independent formulation of
a holographic theory of quantum gravity. The present review incorporates
the necessary background material on geometry of canonical quantum theory,
holography and spacetime thermodynamics, Matrix theory, as well as our
specific proposal for a dynamical theory of geometric quantum mechanics, as
applied to Matrix theory. At the heart of this review is a new analysis of
the conceptual problem of time and the closely related and phenomenologically
relevant problem of vacuum energy in quantum gravity. We also present a
discussion of some observational implications of this new viewpoint on
the problem of vacuum energy.
Fine structure of dark energy and new physics (with M. Kavic and D. Minic)
Adv. High Energy Phys., 2007, 21586 (2007)arXiv:0705.4581 [hep-th]SPIRES Abstract:
Following our recent work on the cosmological constant problem, in this
letter we make a specific proposal regarding the fine structure (i.e.,
the spectrum) of dark energy. The proposal is motivated by a deep analogy
between the blackbody radiation problem, which led to the development
of quantum theory, and the cosmological constant problem, which we
have recently argued calls for a conceptual extension of the quantum
theory. We argue that the fine structure of dark energy is governed by a
Wien distribution, indicating its dual quantum and classical nature. We
discuss a few observational consequences of such a picture of dark energy.
Why there is something so close to nothing: Towards a fundamental theory of the cosmological constant (with D. Minic)
Int. J. Mod. Phys. A, 22, 1797 (2007)arXiv:hep-th/0605105SPIRES Abstract:
The cosmological constant problem is turned around to argue for a new
foundational physics postulate underlying a consistent quantum theory of
gravity and matter, such as string theory. This postulate is a quantum
equivalence principle which demands a consistent gauging of the geometric
structure of canonical quantum theory. We argue that string theory can be
formulated to accommodate such a principle, and that in such a theory the
observed cosmological constant is a fluctuation about a zero value. This
fluctuation arises from an uncertainty relation involving the cosmological
constant and the effective volume of spacetime. The measured, small vacuum
energy is dynamically tied to the large size of the universe, thus violating
naive decoupling between small and large scales. The numerical value is
related to the scale of cosmological supersymmetry breaking, supersymmetry
being needed for a non-perturbative stability of local Minkowski spacetime
regions in the classical regime.
Exploring the vacuum geometry of N = 1 gauge theories (with J. Gray, Y.-H. He, and B. D. Nelson)
Nucl. Phys. B, 750, 1 (2006)arXiv:hep-th/0604208SPIRES Abstract:
Using techniques of algorithmic algebraic geometry, we present a new
and efficient method for explicitly computing the vacuum space of N = 1
gauge theories. We emphasize the importance of finding special geometric
properties of these spaces in connecting phenomenology to guiding principles
descending from high-energy physics. We exemplify the method by addressing
various subsectors of the MSSM. In particular the geometry of the vacuum
space of electroweak theory is described in detail, with and without
right-handed neutrinos. We discuss the impact of our method on the search
for evidence of underlying physics at a higher energy. Finally we describe
how our results can be used to rule out certain top-down constructions of
electroweak physics.
Vacuum geometry and the search for new physics (with J. Gray, Y.-H. He, and B. D. Nelson)
Phys. Lett. B, 638, 253 (2006)arXiv:hep-th/0511062SPIRES Abstract:
We propose a new principle for phenomenology: special geometry in the vacuum
space. New algorithmic methods efficiently compute geometric properties of
the vacuum space of N = 1 supersymmetric gauge theories. We illustrate the
technique on subsectors of the MSSM. The fragility of geometric structure
in the moduli space motivates phenomenologically realistic deformations
of the superpotential. Special geometry in the vacuum may be a signal of
string physics within the low-energy theory.
The Library of Babel: On the origin of gravitational thermodynamics (with V. Balasubramanian, J. de Boer, and J. Simón)
JHEP, 0512, 006 (2005)arXiv:hep-th/0508023SPIRES Abstract:
We show that heavy pure states of gravity can appear to be mixed states to
almost all probes. For AdS5 Schwarzschild black holes, our arguments are
made using the field theory dual to string theory in such spacetimes. Our
results follow from applying information theoretic notions to field theory
operators capable of describing very heavy states in gravity. For half-BPS
states of the theory which are incipient black holes, our account is exact:
typical microstates are described in gravity by a spacetime ``foam'', the
precise details of which are almost invisible to almost all probes. We
show that universal low-energy effective description of a foam of given
global charges is via certain singular spacetime geometries. When one of
the specified charges is the number of D-branes, the effective singular
geometry is the half-BPS ``superstar''. We propose this as the general
mechanism by which the effective thermodynamic character of gravity emerges.
The Library of Babel (with V. Balasubramanian and J. Simón)
Int. J. Mod. Phys. D, 14, 2181 (2005)arXiv:hep-th/0505123SPIRES Essay awarded Honorable Mention in the 2005 Gravity Research Foundation Essay Competition.
Abstract:
We show that heavy pure states of gravity can appear to be mixed states to
almost all probes. Our arguments are made for AdS5 Schwarzschild black
holes using the field theory dual to string theory in such spacetimes. Our
results follow from applying information theoretic notions to field theory
operators capable of describing very heavy states in gravity. For certain
supersymmetric states of the theory, our account is exact: the microstates are
described in gravity by a spacetime ``foam'', the precise details of which are
invisible to almost all probes.
Non-supersymmetric smooth geometries and D1-D5-P bound states (with O. Madden, S. F. Ross, and G. Titchener)
Phys. Rev. D, 71, 124030 (2005)arXiv:hep-th/0504181SPIRES Abstract:
We construct smooth non-supersymmetric soliton solutions with D1-brane,
D5-brane, and momentum charges in type IIB supergravity compactified on
T4×S1, with the charges along the compact
directions. This generalises previous studies of smooth supersymmetric
solutions. The solutions are obtained by considering a known family of
U(1)×U(1) invariant metrics, and studying the conditions
imposed by requiring smoothness. We discuss the relation of our solutions
to states in the CFT describing the D1-D5 system, and describe various
interesting features of the geometry.
Alpha-states in de Sitter space (with J. de Boer and D. Minic)
Phys. Rev. D, 71, 044013 (2005)arXiv:hep-th/0406217SPIRES Abstract:
Field theory in de Sitter space admits a one-parameter family of vacua
determined by a superselection parameter α. Of these vacua, the Euclidean
vacuum uniquely extrapolates to the vacuum of flat Minkowski space. States
which resemble the α-vacua can be constructed as excitations above
the Euclidean vacuum. Such states have modes α(k) which decay faster
that k(1-d)/2. Fields in such states exhibit non-local correlations
when examined from the perspective of fields in the Euclidean vacuum. The
dynamics of such entangled states are fully consistent. If an α-state
with properties that interpolate between an α-vacuum and the Euclidean
vacuum were the initial condition for inflation, a signature for this
may be found in a momentum dependent correction to the inflationary power
spectrum. The functional formalism, which provides the tool for examining
physics in an α-state, extends to fields of other spin. In particular,
the extension to spin-2 may proffer a new class of infrared modifications
to gravitational interactions. The implications of superselection sectors
for the landscape of string vacua are briefly discussed.
Toward a background independent quantum theory of gravity (with D. Minic and C.-H. Tze)
Int. J. Mod. Phys. D, 13, 2307 (2004)arXiv:gr-qc/0406037SPIRES Essay awarded Honorable Mention in the 2004 Gravity Research Foundation Essay Competition.
Abstract:
Any canonical quantum theory can be understood to arise from the
compatibility of the statistical geometry of distinguishable observations
with the canonical Poisson structure of Hamiltonian dynamics. This geometric
perspective offers a novel, background independent non-perturbative
formulation of quantum gravity. We invoke a quantum version of the
equivalence principle, which requires both the statistical and symplectic
geometries of canonical quantum theory to be fully dynamical quantities. Our
approach sheds new light on such basic issues of quantum gravity as the
nature of observables, the problem of time, and the physics of the vacuum. In
particular, the observed numerical smallness of the cosmological constant
can be rationalized in this approach.
Modular matrix models (with Y.-H. He)
To appear in Moonshine conference proceedings.
arXiv:hep-th/0307293SPIRES Abstract:
Inspired by a formal resemblance of certain q-expansions of modular
forms and the master field formalism of matrix models in terms of Cuntz
operators, we construct a Hermitian one-matrix model, which we dub the
"modular matrix model." Together with an N = 1 gauge theory and a
special Calabi-Yau geometry, we find a modular matrix model that naturally
encodes the Klein elliptic j-invariant, and hence, by Moonshine,
the irreducible representations of the Fischer-Griess Monster group.
Deconstructing the cosmological constant (with R. G. Leigh and D. Minic)
Gen. Rel. Grav., 35, 2089, (2003)arXiv:gr-qc/0305072SPIRES Essay awarded Fourth Prize in the 2003 Gravity Research Foundation Essay Competition.
Abstract:
Deconstruction provides a novel way of dealing with the notoriously
difficult ultraviolet problems of four-dimensional gravity. This approach
also naturally leads to a new perspective on the holographic principle,
tying it to the fundamental requirements of unitarity and diffeomorphism
invariance, as well as to a new viewpoint on the cosmological constant
problem. The numerical smallness of the cosmological constant is implied
by a unique combination of holography and supersymmetry, opening a new
window into the fundamental physics of the vacuum.
Deconstruction and holography (with R. G. Leigh and D. Minic)
J. Cosmol. Astropart. Phys., 06, 002 (2003)arXiv:hep-th/0302230SPIRES Abstract:
It was recently pointed out that the physics of a single discrete
gravitational extra dimension exhibits a peculiar UV/IR connection relating
the UV scale to the radius of the effective extra dimension. Here we note
that this non-locality is a manifestation of holography, encoding the
correct scaling of the number of fundamental degrees of freedom of the
UV theory. This in turn relates the Wilsonian RG flow in the UV theory
to the effective gravitational dynamics in the extra dimension. The
relevant holographic c-function is determined by the expression
for the holographic bound. Holography in this context is a result of the
requirements of unitarity and diffeomorphism invariance. We comment on
the relevance of this observation for the cosmological constant problem.
Multi-trace superpotentials vs. Matrix models (with V. Balasubramanian, J. de Boer, B. Feng, Y.-H. He, M.-x. Huang, and A. Naqvi)
Commun. Math. Phys., 242, 361 (2003)arXiv:hep-th/0212082SPIRES Abstract:
We consider N = 1 supersymmetric U(N) field theories in
four dimensions with adjoint chiral matter and a multi-trace tree-level
superpotential. We show that the computation of the effective action
as a function of the glueball superfield localizes to computing matrix
integrals. Unlike the single-trace case, holomorphy and symmetries do
not forbid non-planar contributions. Nevertheless, only a special subset
of the planar diagrams contributes to the exact result. Some of the
data of this subset can be computed from the large-N limit of an
associated multi-trace Matrix model. However, the prescription differs
in important respects from that of Dijkgraaf and Vafa for single-trace
superpotentials in that the field theory effective action is not the
derivative of a multi-trace matrix model free energy. The basic subtlety
involves the correct identification of the field theory glueball as a
variable in the Matrix model, as we show via an auxiliary construction
involving a single-trace matrix model with additional singlet fields
which are integrated out to compute the multi-trace results. Along the
way we also describe a general technique for computing the large-N
limits of multi-trace Matrix models and raise the challenge of finding
the field theories whose effective actions they may compute. Since our
models can be treated as N = 1 deformations of pure N = 2
gauge theory, we show that the effective superpotential that we compute
also follows from the N = 2 Seiberg-Witten solution. Finally, we
observe an interesting connection between multi-trace local theories and
non-local field theory.
The cosmological constant and the deconstruction of gravity (with R. G. Leigh and D. Minic)
Phys. Lett. B, 556, 71 (2003)arXiv:hep-th/0212057SPIRES Abstract:
Witten has presented an argument for the vanishing of the cosmological
constant in 2+1 dimensions. This argument is crucially tied to the specific
properties of (2+1)-dimensional gravity. We argue that this reasoning can be
deconstructed to 3+1 dimensions under certain conditions. Our observation is
also tied to a possibility that there exists a well-defined UV completion of
(3+1)-dimensional gravity.
Non-commutative Chern-Simons for the quantum Hall system and duality (with E. Fradkin and R. G. Leigh)
Nucl. Phys. B, 642, 483 (2002)arXiv:cond-mat/0205653SPIRES Abstract:
The quantum Hall system is known to have two mutually dual Chern-Simons
descriptions, one associated with the hydrodynamics of the electron fluid,
and another associated with the statistics. Recently, Susskind has made
the claim that the hydrodynamic Chern-Simons theory should be considered
to have a non-commutative gauge symmetry. The statistical Chern-Simons
theory has a perturbative momentum expansion. In this paper, we study this
perturbation theory and show that the effective action, although commutative
at leading order, is non-commutative. This conclusion is arrived at through a
careful study of the three-point function of Chern-Simons gauge fields. The
non-commutative gauge symmetry of this system is thus a quantum symmetry,
which we show can only be fully realized only through the inclusion of
all orders in perturbation theory. We discuss the duality between the two
non-commutative descriptions.
The Standard Model on a D-brane (with D. Berenstein and R. G. Leigh)
Phys. Rev. Lett., 88, 071602 (2002)arXiv:hep-ph/0105042SPIRES Abstract:
We present a consistent string theory model which reproduces the Standard
Model, consisting of a D3-brane at a simple orbifold singularity. We
study some simple features of the phenomenology of the model. We find
that the scale of stringy physics must be in the multi-TeV range. There
are natural hierarchies in the fermion spectrum and there are several
possible experimental signatures of the model.
D-branes on singularities: New quivers from old (with D. Berenstein and R. G. Leigh)
Phys. Rev. D, 64, 046011 (2001)arXiv:hep-th/0012050SPIRES Abstract:
In this paper we present simplifying techniques which allow one to
compute the quiver diagrams for various D-branes at (non-Abelian)
orbifold singularities with and without discrete torsion. The main idea
behind the construction is to take the orbifold of an orbifold. Many
interesting discrete groups fit into an exact sequence N →
G → G/N. As such, the orbifold M/G is easier to
compute as (M/N)/(G/N) and we present graphical rules which allow
fast computation given the M/N quiver.
Non-commutative moduli spaces, dielectric tori, and T-duality (with D. Berenstein and R. G. Leigh)
Phys. Lett. B, 493, 162 (2000)arXiv:hep-th/0006168SPIRES Abstract:
We review and extend recent work on the application of the non-commutative
geometric framework to an interpretation of the moduli space of vacua
of certain deformations of N = 4 super Yang-Mills theories. We
present a simple worldsheet calculation that reproduces the field
theory results and sheds some light on the dynamics of the D-brane
bubbles. Different regions of moduli space are associated with D5-branes
of various topologies; singularities in the moduli space are associated
with topology change. T-duality on toroidal topologies maps between mirror
string realizations of the field theory.
Marginal and relevant deformations of N = 4 field theories and non-commutative moduli spaces of vacua (with D. Berenstein and R. G. Leigh)
Nucl. Phys. B, 589, 196 (2000)arXiv:hep-th/0005087SPIRES Abstract:
We study marginal and relevant supersymmetric deformations of the
N = 4 super-Yang-Mills theory in four dimensions. Our primary
innovation is the interpretation of the moduli spaces of vacua of these
theories as non-commutative spaces. The construction of these spaces
relies on the representation theory of the related quantum algebras,
which are obtained from F-term constraints. These field theories
are dual to superstring theories propagating on deformations of the
AdS5×S5 geometry. We study D-branes
propagating in these vacua and introduce the appropriate notion of
algebraic geometry for non-commutative spaces. The resulting moduli
spaces of D-branes have several novel features. In particular, they may be
interpreted as symmetric products of non-commutative spaces. We show how
mirror symmetry between these deformed geometries and orbifold theories
follows from T-duality. Many features of the dual closed string theory
may be identified within the non-commutative algebra. In particular, we
make progress towards understanding the K-theory necessary for backgrounds
where the Neveu-Schwarz antisymmetric tensor of the string is turned on,
and we shed light on some aspects of discrete anomalies based on the
non-commutative geometry.
Far from equilibrium nonconserved growth under a surface diffusion bias (with S. Das Sarma and C. J. Lanczycki)
Phys. Rev. E, 54, 4755 (1996) Abstract:
We study a generic one-dimensional atomistic model of interface growth
under random ballistic deposition in the presence of a surface diffusion
bias allowing for surface overhangs and bulk vacancies. We find that
various diffusion bias induced surface instabilities recently found in the
solid-on-solid approximation of kinetic growth are absent in the generic
model with the usual statistically self-affine Kardar-Parisi-Zhang scaling
dominating the surface morphology. For strong biases and high temperatures,
the growing surface resembles the zero temperature ballistic growth without
a diffusion bias. The growth front morphologies show intricate flamelike
nonlocal structures not typically present in self-affine surfaces. This
indicates that the standard coarse-grained single-variable description of
the growing film by its local surface height coordinate misses an important
qualitative feature, namely, a novel flamelike roughening behavior along
vertical faces of the growth front.
Erdös Number: 4
P. Erdös → M. Herzog → R. Donagi → Y.-H. He → V. Jejjala