15,013 research outputs found
Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
It is well known that a local, unitary Poincare-invariant 2D QFT with a
global scaling symmetry and a discrete non-negative spectrum of scaling
dimensions necessarily has both a left and a right local conformal symmetry. In
this paper we consider a chiral situation beginning with only a left global
scaling symmetry and do not assume Lorentz invariance. We find that a left
conformal symmetry is still implied, while right translations are enhanced
either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.Comment: 6 pages, no figures. v2: reference added, minor typos correcte
Deformations of Closed Strings and Topological Open Membranes
We study deformations of topological closed strings. A well-known example is
the perturbation of a topological closed string by itself, where the
associative OPE product is deformed, and which is governed by the WDVV
equations. Our main interest will be closed strings that arise as the boundary
theory for topological open membranes, where the boundary string is deformed by
the bulk membrane operators. The main example is the topological open membrane
theory with a nonzero 3-form field in the bulk. In this case the Lie bracket of
the current algebra is deformed, leading in general to a correction of the
Jacobi identity. We identify these deformations in terms of deformation theory.
To this end we describe the deformation of the algebraic structure of the
closed string, given by the BRST operator, the associative product and the Lie
bracket. Quite remarkably, we find that there are three classes of deformations
for the closed string, two of which are exemplified by the WDVV theory and the
topological open membrane. The third class remains largely mysterious, as we
have no explicit example.Comment: 50 pages, LaTeX; V2: minor changes, 2 references added, V3: typos
corrected, signs added, modified discussion on higher correlator
Scalable Recommendation with Poisson Factorization
We develop a Bayesian Poisson matrix factorization model for forming
recommendations from sparse user behavior data. These data are large user/item
matrices where each user has provided feedback on only a small subset of items,
either explicitly (e.g., through star ratings) or implicitly (e.g., through
views or purchases). In contrast to traditional matrix factorization
approaches, Poisson factorization implicitly models each user's limited
attention to consume items. Moreover, because of the mathematical form of the
Poisson likelihood, the model needs only to explicitly consider the observed
entries in the matrix, leading to both scalable computation and good predictive
performance. We develop a variational inference algorithm for approximate
posterior inference that scales up to massive data sets. This is an efficient
algorithm that iterates over the observed entries and adjusts an approximate
posterior over the user/item representations. We apply our method to large
real-world user data containing users rating movies, users listening to songs,
and users reading scientific papers. In all these settings, Bayesian Poisson
factorization outperforms state-of-the-art matrix factorization methods
Einstein gravity from ANEC correlators
We study correlation functions with multiple averaged null energy (ANEC)
operators in conformal field theories. For large CFTs with a large gap to
higher spin operators, we show that the OPE between a local operator and the
ANEC can be recast as a particularly simple differential operator acting on the
local operator. This operator is simple enough that we can resum it and obtain
the finite distance OPE. Under the large - large gap assumptions, the
vanishing of the commutator of ANEC operators tightly constrains the OPE
coefficients of the theory. An important example of this phenomenon is the
conclusion that in . This implies that the bulk dual of such a CFT
is semi-classical Einstein-gravity with minimally coupled matter.Comment: 32 pages + appendices, 6 figures; v2:typos corrected and a comment
added in introductio
Warped Weyl fermion partition functions
Warped conformal field theories (WCFTs) are a novel class of non-relativistic
theories. A simple, yet non-trivial, example of such theory is a massive Weyl
fermion in -dimensions, which we study in detail. We derive general
properties of the spectrum and modular properties of partition functions of
WCFTs. The periodic (Ramond) sector of this fermionic system is non-trivial,
and we build two novel partition functions for this sector which have no
counterpart in a CFT. The thermodynamical properties of WCFTs are revisited
in the canonical and micro-canonical ensemble.Comment: 41 page
Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars
We apply a small magnetic field to strongly interacting matter with a gravity
dual description as an electron star. These systems are both metallic and
quantum critical at low energies. The resulting quantum oscillations are shown
to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It
is seen that only fermions at a single radius in the electron star contribute
to the oscillations. We proceed to show that the Fermi surface area extracted
from the quantum oscillations does not obey the simplest statement of the
Luttinger theorem, that is, it is not universally proportional to the total
charge density. It follows that our system is a non-Fermi liquid that
nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the
Luttinger count is recovered via a field theoretic description involving a
continuum of `smeared' fermionic excitations.Comment: 1+15 pages. 4 figures. v2 minor change to discussio
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