2,204 research outputs found
Dynamical tachyons on fuzzy spheres
We study the spectrum of off-diagonal fluctuations between displaced fuzzy
spheres in the BMN plane wave matrix model. The displacement is along the plane
of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles
classical tachyons develop and that the spectrum of these modes can be computed
analytically. These tachyons can be related to the familiar Nielsen-Olesen
instabilities in Yang-Mills theory on a constant magnetic background. Many
features of the problem become more apparent when we compare with maximally
supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We
also set up a simple oscillatory trajectory on the displacement between the
fuzzy spheres and study the dynamics of the modes as they become tachyonic for
part of the oscillations. We speculate on their role regarding the possible
thermalization of the system.Comment: 34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added
reference
The Photon Dispersion as an Indicator for New Physics ?
We first comment on the search for a deviation from the linear photon
dispersion relation, in particular based on cosmic photons from Gamma Ray
Bursts. Then we consider the non-commutative space as a theoretical concept
that could lead to such a deviation, which would be a manifestation of Lorentz
Invariance Violation. In particular we review a numerical study of pure U(1)
gauge theory in a 4d non-commutative space. Starting from a finite lattice, we
explore the phase diagram and the extrapolation to the continuum and infinite
volume. These simultaneous limits - taken at fixed non-commutativity - lead to
a phase of broken Poincare symmetry, where the photon appears to be IR stable,
despite a negative IR divergence to one loop.Comment: 8 pages, 4 figures, talk presented at the VI International Workshop
on the Dark Side of the Universe, Leon (Mexico), June 1-6, 2010. References
adde
Two-dimensional models as testing ground for principles and concepts of local quantum physics
In the past two-dimensional models of QFT have served as theoretical
laboratories for testing new concepts under mathematically controllable
condition. In more recent times low-dimensional models (e.g. chiral models,
factorizing models) often have been treated by special recipes in a way which
sometimes led to a loss of unity of QFT. In the present work I try to
counteract this apartheid tendency by reviewing past results within the setting
of the general principles of QFT. To this I add two new ideas: (1) a modular
interpretation of the chiral model Diff(S)-covariance with a close connection
to the recently formulated local covariance principle for QFT in curved
spacetime and (2) a derivation of the chiral model temperature duality from a
suitable operator formulation of the angular Wick rotation (in analogy to the
Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational
chiral theories. The SL(2,Z) modular Verlinde relation is a special case of
this thermal duality and (within the family of rational models) the matrix S
appearing in the thermal duality relation becomes identified with the
statistics character matrix S. The relevant angular Euclideanization'' is done
in the setting of the Tomita-Takesaki modular formalism of operator algebras.
I find it appropriate to dedicate this work to the memory of J. A. Swieca
with whom I shared the interest in two-dimensional models as a testing ground
for QFT for more than one decade.
This is a significantly extended version of an ``Encyclopedia of Mathematical
Physics'' contribution hep-th/0502125.Comment: 55 pages, removal of some typos in section
Multiple Membranes in M-theory
We review developments in the theory of multiple, parallel membranes in
M-theory. After discussing the inherent difficulties pertaining to a maximally
supersymmetric lagrangian formulation with the appropriate field content and
symmetries, we discuss how introducing the concept of 3-algebras allows for
such a description. Different choices of 3-algebras lead to distinct classes of
2+1 dimensional theories with varying degrees of supersymmetry. We then
describe how these are equivalent to a type of conventional superconformal
Chern-Simons gauge theories at level k, coupled to bifundamental matter.
Analysing the physical properties of these theories leads to the identification
of a certain subclass of models with configurations of M2-branes in Z_k
orbifolds of M-theory. In addition these models give rise to a whole new sector
of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We
also discuss mass deformations, higher derivative corrections as well as the
possibility of extracting information about M5-brane physics.Comment: 180 pages, 3 figures, Latex; v2: various typos corrected,
clarifications, references and acknowledgements added, title modified,
submitted to Physics Report
Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition
of noncommutative Yang-Mills theory: the continuum limit is approached at large
by performing suitable double scaling limits, in which non-planar
contributions are no longer suppressed. We consider here the two-dimensional
case, trying to recover within this framework the exact results recently
obtained by means of Morita equivalence. We present a rather explicit
construction of classical gauge theories on noncommutative toroidal lattice for
general topological charges. After discussing the limiting procedures to
recover the theory on the noncommutative torus and on the noncommutative plane,
we focus our attention on the classical solutions of the related TEK models. We
solve the equations of motion and we find the configurations having finite
action in the relevant double scaling limits. They can be explicitly described
in terms of twist-eaters and they exactly correspond to the instanton solutions
that are seen to dominate the partition function on the noncommutative torus.
Fluxons on the noncommutative plane are recovered as well. We also discuss how
the highly non-trivial structure of the exact partition function can emerge
from a direct matrix model computation. The quantum consistency of the TEK
formulation is eventually checked by computing Wilson loops in a particular
limit.Comment: 41 pages, JHEP3. Minor corrections, references adde
Non-Liquid Cellular States
The existence of quantum non-liquid states and fracton orders, both gapped
and gapless states, challenges our understanding of phases of entangled matter.
We generalize Wen's cellular topological states to liquid or non-liquid
cellular states. We propose a mechanism to construct more general non-abelian
states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces
as extended defects in a cellular network, including defects of
higher-symmetries. Our approach also includes the anyonic particle/string
condensation and composite string (p-string)/membrane condensations. This also
shows gluing the familiar extended topological quantum field theory or
conformal field theory data via topology, geometry, and renormalization
consistency criteria (via certain modified group cohomology or cobordism theory
data) in a tensor network can still guide us to analyze the non-liquid states.
(Part of the abelian construction can be understood from the K-matrix
Chern-Simons theory approach and coupled-layer-by-junction constructions.) This
may also lead us toward a unifying framework for quantum systems of both
higher-symmetries and sub-system/sub-dimensional symmetries.Comment: 42 pages. Subtitle: Gluing Gauge-(Higher)-Symmetry-Breaking vs
-Extension Interfacial Defect
Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
In this paper we discuss behaviors of entanglement entropy between two
interacting CFTs and its holographic interpretation using the AdS/CFT
correspondence. We explicitly perform analytical calculations of entanglement
entropy between two free scalar field theories which are interacting with each
other in both static and time-dependent ways. We also conjecture a holographic
calculation of entanglement entropy between two interacting
super Yang-Mills theories by introducing a minimal surface in the S
direction, instead of the AdS direction. This offers a possible
generalization of holographic entanglement entropy.Comment: 37 pages, 7 figures, v2: typos corrected, references added, v3: a
ref. + a clarification note about minimal surfaces adde
Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
We consider states with large angular momentum to facilitate the study of the
M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between
M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with
gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this
regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes
the gravity side difficult, while the CFT is strongly coupled and the planar
approximation is not applicable. To overcome these difficulties, we focus on
states on the gravity side with large angular momentum J>>1 and identify the
dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this
sector. Natural approximation schemes arise on both sides thanks to the
presence of the small parameter 1/J. On the AdS side, we use the matrix model
of M-theory on the maximally supersymmetric pp-wave background with matrices of
size J/k. A perturbative treatment of this matrix model provides a good
approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT
side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer
type expansion arises naturally for large J in spite of the theory being
strongly coupled. The energy spectra on the two sides agree at leading order.
This provides a non-trivial test of the AdS_4/CFT_3 correspondence including
near-BPS observables associated with membrane degrees of freedom, thus
verifying the duality beyond the previously studied sectors corresponding to
either BPS observables or the type IIA string regime.Comment: 67 pages, 5 figures; V2: minor changes, references adde
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