arXiv subjects

Alfred D. Shapere

Publications and source records attributed to Alfred D. Shapere.

At least 19 recordsLinked to original sources

arXiv2023

Global Symmetries, Code Ensembles, and Sums Over Geometries

We consider Abelian topological quantum field theories (TQFTs) in 3d and show that gaugings of invertible global symmetries naturally give rise to additive codes. These codes emerge as nonanomalous subgroups of the 1-form symmetry group, parameterizing the fusion rules of condensable TQFT anyons. The boundary theories dual to TQFTs with the anyons condensed, i.e. with the corresponding symmetry subgroup gauged, are "code" conformal field theories (CFTs). This observation bridges together, in the holographic sense, results on 1-form symmetries of 3d TQFTs with developments connecting codes to 2d CFTs. Building on this relationship, we proceed to consider the ensemble of maximal gaugings (topological boundary conditions) in a general, not necessarily Abelian 3d TQFT, and propose that the resulting ensemble of boundary CFTs has a holographic description as a gravitational theory -- the bulk TQFT summed over topologies.

hep-th↗

arXiv2023

Holographic description of Narain CFTs and their code-based ensembles

We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central charge $c=n$, and a sum of $(U(1) \times U(1))^n$ Chern-Simons theories on different handlebody topologies. We begin by reviewing the general relation of additive codes to Narain CFTs. Then we describe a holographic duality between any given Narain theory and a pure Chern-Simons theory on a handlebody manifold. We proceed to consider an ensemble of Narain theories, defined in terms of an ensemble of codes of length $n$ over ${\mathbb Z}_k \times {\mathbb Z}_k$ for prime $k$. We show that averaging over this ensemble is holographically dual to a level-$k$ $(U(1) \times U(1))^n$ Chern-Simons theory, summed over a finite number of inequivalent classes of handlebody topologies. In the limit of large $k$ the ensemble approaches the ensemble of all Narain theories, and its bulk dual becomes equivalent to "U(1)-gravity" - the sum of the pertubative part of the Chern-Simons wavefunction over all possible handlebodies - providing a bulk microscopic definition for this theory. Finally, we reformulate the sum over handlebodies in terms of Hecke operators, paving the way for generalizations.

hep-th↗

arXiv2019

Regularizations of Time Crystal Dynamics

We demonstrate that non-convex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets - ``Sisyphus dynamics'' - is a generic consequence. In quantum mechanics this microstructure can be blurred, leaving entirely regular behavior.

cond-mat.stat-mech↗

arXiv2016

Skyrmions and Hall Transport

We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the 2+1 dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data, and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.

cond-mat.str-el↗

arXiv2014

Bounds on Operator Dimensions in 2D Conformal Field Theories

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $Δ_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $Δ_1$: $Δ_2 \leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $Δ_3$, and present a method for deriving bounds on $Δ_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $Δ_n \leq \frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the gravitational implications of these results.

hep-th↗

arXiv2014

A counterexample to the a-'theorem'

The conclusion of the original paper was wrong, due to the incorrect assumption that the low-energy limit at the strongly-coupled point consists of a single, coupled SCFT. By taking into account the fact that the low-energy limit consists of multiple decoupled parts, it was later shown in arXiv:1011.4568 that there is no violation of the a-theorem in this system. Furthermore, the a-theorem itself was convincingly demonstrated in arXiv:1107.3987, and the argument presented there has been further refined. The rest of this paper is kept as it was, for some parts of the discussions might still be of interest. Original abstract: We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge 'a' increases. The flow connects the maximally superconformal point of an N=2 gauge theory with gauge group SU(N+1) and N_f=2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with N_f=2N massless flavors in the infrared. Our example does not contradict the proof of the a-theorem via a-maximization, due to the presence of accidental symmetries in the infrared limit. Nor does it contradict the holographic a-theorem, because these gauge theories do not possess weakly-curved holographic duals.

hep-th↗

arXiv2012

Models of Topology Change

We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of entanglement entropy production. We discuss approximate realization of boundary conditions through appropriate interactions, thus suggesting a route to possible experimental realization. We give a theoretical application to quantization of singular Hamiltonians, and give tangible form to the "many worlds" interpretation of wave functions.

hep-th↗

arXiv2011

On Dumb Holes and their Gravity Duals

Inhomogeneous fluid flows which become supersonic are known to produce acoustic analogs of ergoregions and horizons. This leads to Hawking-like radiation of phonons with a temperature essentially given by the gradient of the velocity at the horizon. We find such acoustic dumb holes in charged conformal fluids and use the fluid-gravity correspondence to construct dual gravity solutions. A class of quasinormal modes around these gravitational backgrounds perceive a horizon. Upon quantization, this implies a thermal spectrum for these modes.

hep-th↗

arXiv2008

Quiver Topology and RG Dynamics

Renormalization group flows of quiver gauge theories play a central role in determining the low-energy properties of string vacua. We demonstrate that useful predictions about the RG dynamics of a quiver gauge theory may be extracted from the global structure of its quiver diagram. For quiver theories of a certain type, we develop an efficient and practical method for determining which superpotential deformations generate a flow to an interacting conformal fixed point.

hep-th↗

arXiv2008

Central charges of N=2 superconformal field theories in four dimensions

We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a-c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.

hep-th↗

arXiv2005

Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches

We study the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries, which potentially describe the Coulomb branches of N=2 supersymmetric field theories in four dimensions. We show that this classification is equivalent to the solution of a set of polynomial equations by using an integrability condition for the central charge, scale invariance, constraints coming from demanding single-valuedness of physical quantities on the Coulomb branch, and properties of massless BPS states at singularities. We find solutions corresponding to lagrangian scale invariant theories--including the scale invariant G_2 theory not found before in the literature--as well as many new isolated solutions (having no marginal deformations). All our scale-invariant RSK geometries are consistent with an interpretation as effective theories of N=2 superconformal field theories, and, where we can check, turn out to exist as quantum field theories.

hep-th↗

arXiv2003

Inelastic Black Hole Production and Large Extra Dimensions

Black hole production in elementary particle collisions is among the most promising probes of large extra spacetime dimensions. Studies of black holes at particle colliders have assumed that all of the incoming energy is captured in the resulting black hole. We incorporate the inelasticity inherent in such processes and determine the prospects for discovering black holes in colliders and cosmic ray experiments, employing a dynamical model of Hawking evolution. At the Large Hadron Collider, inelasticity reduces rates by factors of 10^3 to 10^6 in the accessible parameter space, moderating, but not eliminating, hopes for black hole discovery. At the Pierre Auger Observatory, rates are suppressed by a factor of 10. We evaluate the impact of cosmic ray observations on collider prospects.

hep-ph↗

arXiv2003

Quest for Black Holes and Superstring Excitations in Cosmic Ray Data

In this talk we discuss aspects of TeV-scale gravitational collapse to black holes and string balls and their subsequent evaporation. Special emphasis is placed on the interplay of the string/black hole correspondence principle. These ideas are then explored in the context of cosmic ray physics. First, the potential for observing showers mediated by black holes or superstring excitations is examined. Next, existing data from neutrino telescopes are used to constrain the parameter space for the unseen dimensions of the universe. Finally, we close with a discussion of future prospects.

hep-ph↗

arXiv2003

Fuzzy Spheres in pp Wave Matrix String Theory

The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For M g_s << 1, the matrix string theory is conventional; only the degrees of freedom in the Cartan subalgebra contribute, and the theory reduces to copies of the perturbative string. For M g_s >> 1, the theory admits degenerate vacua representing fundamental strings blown up into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of small fluctuations around these vacua. Around such a vacuum all N-squared degrees of freedom are excited with comparable energies. The spectrum of masses has a spacing which is independent of the radius of the fuzzy sphere, in agreement with expected behaviour of continuum giant gravitons. Furthermore, for fuzzy spheres characterized by reducible representations of SU(2) and vanishing Wilson lines, the boundary conditions on the field are characterized by a set of continuous angles which shows that generically the blown up strings do not ``close''.

hep-th↗

arXiv2003

Updated Limits on TeV-Scale Gravity from Absence of Neutrino Cosmic Ray Showers Mediated by Black Holes

We revise existing limits on the D-dimensional Planck scale M_D from the nonobservation of microscopic black holes produced by high energy cosmic neutrinos in scenarios with D=4+n large extra dimensions. Previous studies have neglected the energy radiated in gravitational waves by the multipole moments of the incoming shock waves. We include the effects of energy loss, as well as form factors for black hole production and recent null results from cosmic ray detectors. For n>4, we obtain M_D > 1.0 - 1.4 TeV. These bounds are among the most stringent and conservative to date.

hep-ph↗

arXiv2002

Neutrino Bounds on Astrophysical Sources and New Physics

Ultra-high energy cosmic neutrinos are incisive probes of both astrophysical sources and new TeV-scale physics. Such neutrinos would create extensive air showers deep in the atmosphere. The absence of such showers implies upper limits on incoming neutrino fluxes and cross sections. Combining the exposures of AGASA, the largest existing ground array, with the exposure of the Fly's Eye fluorescence detector integrated over all its operating epochs, we derive 95% CL bounds that substantially improve existing limits. We begin with model-independent bounds on astrophysical fluxes, assuming standard model cross sections, and model-independent bounds on new physics cross sections, assuming a conservative cosmogenic flux. We then derive model-dependent constraints on new components of neutrino flux for several assumed power spectra, and we update bounds on the fundamental Planck scale M_D in extra dimension scenarios from black hole production. For large numbers of extra dimensions, we find M_D > 2.0 (1.1) TeV for \mbhmin = M_D (5 M_D), comparable to or exceeding the most stringent constraints to date.

hep-ph↗

arXiv2002

Phenomenology of Randall-Sundrum Black Holes

We explore the phenomenology of microscopic black holes in the $S^1/Z_2$ Randall-Sundrum (RS) model. We consider the canonical framework in which both gauge and matter fields are confined to the brane and only gravity spills into the extra dimension. The model is characterized by two parameters, the mass of the first massive graviton $(m_1)$, and the curvature $1/\ell$ of the RS anti-de Sitter space. We compute the sensitivity of present and future cosmic ray experiments to various regions of $\ell$ and $m_1,$ and compare with that of Runs I and II at the Tevatron. As part of our phenomenological analysis, we examine constraints placed on $\ell$ by AdS/CFT considerations.

hep-ph↗

arXiv2002

Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultra-high energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With n \ge 4 extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.

hep-ph↗