22 research outputs found
Hawking-Page transition in holographic massive gravity
We study the Hawking-Page transition in a holographic model of field theories
with momentum dissipation. We find that the deconfinement temperature strictly
decreases as momentum dissipation is increased. For sufficiently strong
momentum dissipation, the critical temperature goes to zero, indicating a
zero-temperature deconfinement transition in the dual field theory.Comment: 17 pages, 1 figure, uncomment \newcommand*{\ShowCalculations}{} in
the tex file for additional details. Journal version (PRD). Presentation
clarified, reference added, and line spacing and title update
Folding Branes
We study classical dynamics of a probe Dp-brane moving in a background
sourced by a stack of Dp-branes. In this context the physics is similar to that
of the effective action for open-string tachyon condensation, but with a
power-law runaway potential. We show that small inhomogeneous ripples of the
probe brane embedding grow with time, leading to folding of the brane as it
moves. We give a full nonlinear analytical treatment of inhomogeneous brane
dynamics, suitable for the Dirac-Born-Infeld + Wess-Zumino theory with
arbitrary runaway potential, in the case where the source branes are BPS. In
the near-horizon geometry, the inhomogeneous brane motion has a dual
description in terms of free streaming of massive relativistic test particles
originating from the initial hypersurface of the probe brane. We discuss
limitations of the effective action description around loci of self-crossing of
the probe brane (caustics). We also discuss the effect of brane folding in
application to the theory of cosmological fluctuations in string theory
inflation.Comment: 15 pages, 2 figures, LaTe
Bulk viscosity and spectral functions in QCD
We examine the behavior of the spectral function for the trace of the stress
tensor in QCD in the two regimes where it is possible to make analytical
progress; weak coupling, and close to a second order QCD phase transition. We
determine the behavior of the bulk viscosity in each regime. We discuss the
problem of analytic continuation of the (lattice) Euclidean correlation
function to determine the spectral function. In each case the spectral function
has a narrow peak at small frequency; its shape would be challenging to extract
accurately from lattice data with error bars.Comment: 15 pages with 5 figures. Clarified discussion, published versio
What Algorithms can Transformers Learn? A Study in Length Generalization
Large language models exhibit surprising emergent generalization properties,
yet also struggle on many simple reasoning tasks such as arithmetic and parity.
This raises the question of if and when Transformer models can learn the true
algorithm for solving a task. We study the scope of Transformers' abilities in
the specific setting of length generalization on algorithmic tasks. Here, we
propose a unifying framework to understand when and how Transformers can
exhibit strong length generalization on a given task. Specifically, we leverage
RASP (Weiss et al., 2021) -- a programming language designed for the
computational model of a Transformer -- and introduce the RASP-Generalization
Conjecture: Transformers tend to length generalize on a task if the task can be
solved by a short RASP program which works for all input lengths. This simple
conjecture remarkably captures most known instances of length generalization on
algorithmic tasks. Moreover, we leverage our insights to drastically improve
generalization performance on traditionally hard tasks (such as parity and
addition). On the theoretical side, we give a simple example where the
"min-degree-interpolator" model of learning from Abbe et al. (2023) does not
correctly predict Transformers' out-of-distribution behavior, but our
conjecture does. Overall, our work provides a novel perspective on the
mechanisms of compositional generalization and the algorithmic capabilities of
Transformers.Comment: Preprin
Hall viscosity from gauge/gravity duality
In (2+1)-dimensional systems with broken parity, there exists yet another
transport coefficient, appearing at the same order as the shear viscosity in
the hydrodynamic derivative expansion. In condensed matter physics, it is
referred to as "Hall viscosity". We consider a simple holographic realization
of a (2+1)-dimensional isotropic fluid with broken spatial parity. Using
techniques of fluid/gravity correspondence, we uncover that the holographic
fluid possesses a nonzero Hall viscosity, whose value only depends on the
near-horizon region of the background. We also write down a Kubo's formula for
the Hall viscosity. We confirm our results by directly computing the Hall
viscosity using the formula.Comment: 12 page
The Viscosity Bound Conjecture and Hydrodynamics of M2-Brane Theory at Finite Chemical Potential
Kovtun, Son and Starinets have conjectured that the viscosity to entropy
density ratio is always bounded from below by a universal multiple of
i.e., for all forms of matter. Mysteriously, the
proposed viscosity bound appears to be saturated in all computations done
whenever a supergravity dual is available. We consider the near horizon limit
of a stack of M2-branes in the grand canonical ensemble at finite R-charge
densities, corresponding to non-zero angular momentum in the bulk. The
corresponding four-dimensional R-charged black hole in Anti-de Sitter space
provides a holographic dual in which various transport coefficients can be
calculated. We find that the shear viscosity increases as soon as a background
R-charge density is turned on. We numerically compute the few first corrections
to the shear viscosity to entropy density ratio and surprisingly
discover that up to fourth order all corrections originating from a non-zero
chemical potential vanish, leaving the bound saturated. This is a sharp signal
in favor of the saturation of the viscosity bound for event horizons even in
the presence of some finite background field strength. We discuss implications
of this observation for the conjectured bound.Comment: LaTeX, 26+1 Pages, 4 Figures, Version 2: references adde