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 $N$ 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 $N$ - 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 $a=c$ in $d=4$. 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 $(1+1)$-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$_2$. 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