arXiv subjects

David A. McGady

Publications and source records attributed to David A. McGady.

At least 19 recordsLinked to original sources

arXiv2021

Backreaction of Schwinger pair creation in massive QED$_2$

Particle-antiparticle pairs can be produced by background electric fields via the Schwinger mechanism provided they are unconfined. If, as in QED in (3+1)-$d$ these particles are massive, the particle production rate is exponentially suppressed below a threshold field strength. Above this threshold, the energy for pair creation must come from the electric field itself which ought to eventually relax to the threshold strength. Calculating this relaxation in a self-consistent manner, however, is difficult. Chu and Vachaspati addressed this problem in the context of capacitor discharge in massless QED$_2$ [1] by utilizing bosonization in two-dimensions. When the bare fermions are massless, the dual bosonized theory is free and capacitor discharge can be analyzed exactly [1], however, special care is required in its interpretation given that the theory exhibits confinement. In this paper we reinterpret the findings of [1], where the capacitors Schwinger-discharge via electrically neutral dipolar meson-production, and generalize this to the case where the fermions have bare masses. Crucially, we note that when the initial charge of the capacitor is large compared to the charge of the fermions, $Q \gg e$, the classical equation of motion for the bosonized model accurately characterizes the dynamics of discharge. For massless QED$_2$, we find that the discharge is suppressed below a critical plate separation that is commensurate with the length scale associated with the meson dipole moment. For massive QED$_2$, we find in addition, a mass threshold familiar from (3+1)-$d$, and show the electric field relaxes to a final steady state with a magnitude proportional to the initial charge. We discuss the wider implications of our findings and identify challenges in extending this treatment to higher dimensions.

hep-th↗

arXiv2021

Ultralight Fermionic Dark Matter

Conventional lore from Tremaine and Gunn excludes fermionic dark matter lighter than a few hundred eV, based on the Pauli exclusion principle. We highlight a simple way of evading this bound with a large number of species that leads to numerous non-trivial consequences. In this scenario there are many distinct species of fermions with quasi-degenerate masses and no couplings to the standard model. Nonetheless, gravitational interactions lead to constraints from measurements at the LHC, of cosmic rays, of supernovae, and of black hole spins and lifetimes. We find that the LHC constrains the number of distinct species, bosons or fermions lighter than $\sim 500$ GeV, to be $N \lesssim 10^{62}$. This, in particular, implies that roughly degenerate fermionic dark matter must be heavier than $\sim 10^{-14}$ eV, which thus relaxes the Tremaine-Gunn bound by $\sim 16$ orders of magnitude. Slightly weaker constraints applying to masses up to $\sim100$ TeV exist from cosmic ray measurements while various constraints on masses $\lesssim10^{-10}$ eV apply from black hole observations. We consider a variety of phenomenological bounds on the number of species of particles. Finally, we note that there exist theoretical considerations regarding quantum gravity which could impose more severe constraints that may limit the number of physical states to $N\lesssim 10^{32}$.

hep-ph↗

arXiv2020

Modular Forms on the Double Half-Plane

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.

math.NT↗

arXiv2019

Black hole evaporation and semiclassicality at large D

Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large $D$, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds come from demanding that the rate of change of the geometry is small and that black holes scramble information faster than they evaporate. This is a consequence of the enormous power of Hawking radiation in $D$-dimensions due to the large available phase space and the resulting minuscule evaporation times. Asymptotically, only black holes with entropies $S \geq D^{D+3} \log D$ are semiclassical. We comment on implications for realistic quantum gravity models in $D \leq 26$ as well as relations to bounds on theories with a large number of gravitationally interacting light species.

hep-th↗

arXiv2019

L-functions for Meromorphic Modular Forms and Sum Rules in Conformal Field Theory

We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of T-reflection, and (iii) express central charges in two-dimensional conformal field theories (2d CFT) as a literal sum over the states in the CFTs spectrum. When a modular form has an order-$p$ pole away from cusps, its $q$-series coefficients grow as $n^{p-1} e^{2 πn t}$ for $t \geq \sqrt{3}/2$. Its L-function must be regularized. We define such L-functions by a deformed Mellin transform. We study the L-functions of logarithmic derivatives of modular forms.L-functions of logarithmic derivatives of Borcherds products reveal a new relationship between Hurwitz class numbers and traces of singular moduli. If we can write 2d CFT path integrals as infinite products, our L-functions confirm T-reflection predictions and relate central charges to regularized sums over the states in a CFTs spectrum. Equating central charges, which are a proxy for the number of degrees of freedom in a theory, directly to a sum over states in these CFTs is new and relies on our regularization of such sums that generally exhibit exponential (Hagedorn) divergences.

hep-th↗

arXiv2018

Temperature-reflection II: Modular Invariance and T-reflection

In this paper, we present robust evidence that general finite temperature quantum field theory (QFT) path integrals are invariant under reflecting temperatures to negative values (T-reflection), up to a possible anomaly phase. Our main focus is on two-dimensional conformal field theories (2d CFTs) on the two-torus. Modular invariance for 2d CFT path integrals follows from demanding invariance under redundant encodings of the two-torus shape in the path integral. We emphasize that identical logic implies 2d CFTs are invariant under T-reflection, up to phases. We compute T-reflection anomaly phases for certain 2d CFT path integrals via a continuation, and via an extension of modular forms from the upper half-plane to the double half-plane. Crucially, they perfectly agree. Requiring QFT path integrals to be invariant under redundant encodings of the spacetime geometry implies (i) that 2d CFTs are both modular and T-reflection invariant and (ii) that general QFT path integrals are invariant under T-reflection. This quite board argument suggests T-reflection phases may indicate previously unnoticed anomalies and consistency conditions for general QFT.

hep-th↗

arXiv2017

Temperature-reflection I: field theory, ensembles, and interactions

In this paper, we revisit the claim that many partition functions are invariant under reflecting temperatures to negative values (T-reflection). The goal of this paper is to demarcate which partition functions should be invariant under T-reflection, and why. Our main claim is that finite-temperature path integrals for quantum field theories (QFTs) should be T-reflection invariant. Because multi-particle partition functions are equal to Euclidean path integrals for QFTs, we expect them to be T-reflection invariant. Single-particle partition functions though are often not invariant under T-reflection. Several exactly solvable systems are non-invariant under naive T-reflection, but are likely invariant under an extended T-reflection. We give example systems that are T-reflection invariant but are (1) non-unitary, (2) chiral, (3) interacting, (4) non-supersymmetric, or (5) non-conformal, and (6) argue that T-reflection is unrelated to time-reversal. Finally, we study the interplay between T-reflection and perturbation theory in the anharmonic harmonic oscillator in quantum mechanics and in Yang-Mills in four-dimensions. This is the first in a series of papers on temperature-reflections.

hep-th↗

arXiv2017

Short-distance Schwinger-mechanism and chiral symmetry

In this paper, we study Schwinger pair production of charged massless particles in constant electric fields of finite-extent. Exploiting a map from the Dirac and Klein-Gordon equation to the harmonic oscillator, we find exact pair production rates for massless fermions and scalars. Pair production rates depend only on the ratio between the capacitor plate separation, $\ell$, and the length-scale of the force-field, $\ell_F$. Chirality ensures that fermion production smoothly vanishes with $\ell/\ell_F$. Scalar pair production though diverges exponentially quickly in this limit. The same limit of the smooth tanh-potential does not diverge; divergences seem tied to singularities in current and charge densities.

hep-th↗

arXiv2016

Spectral sum rules for confining large-N theories

We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale $Λ^{-1}$. Our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.

hep-th↗

arXiv2015

Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter

In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.

hep-th↗

arXiv2015

A 4D-2D equivalence for large-N Yang-Mills theory

General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory.

hep-th↗

arXiv2015

Bose-Fermi Degeneracies in Large $N$ Adjoint QCD

We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L \sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.

hep-th↗

arXiv2014

Casimir energy of confining large $N$ gauge theories

Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The $N=\infty$ renormalized vacuum energy turns out to vanish in all of the large $N$ gauge theories we have examined, confirming a striking prediction of temperature-reflection symmetry.

hep-th↗

arXiv2014

Higher-spin massless S-matrices in four-dimensions

On-shell, analytic S-matrix elements in massless theories are constructed from a finite set of primitive three-point amplitudes, which are fixed by Poincare invariance up to an overall numerical constant. We classify \emph{all} such three-point amplitudes in four-dimensions. Imposing the simplest incarnation of Locality and Unitarity on four-particle amplitudes constructed from these three-particle amplitudes rules out all but an extremely small subset of interactions among higher-spin massless states. Notably, the equivalence principle, and the Weinberg-Witten theorem, are simple corollaries of this principle. Further, no massless states with helicity larger than two may consistently interact with massless gravitons. Chromodynamics, electrodynamics, Yukawa and $ϕ^3$-theories are the only marginal and relevant interactions between massless states. Finally, we show that supersymmetry naturally emerges as a consistency condition on four-particle amplitudes involving spin-3/2 states, which must always interact gravitationally.

hep-th↗

arXiv2014

Gravitons, Bose-symmetry, and Bonus-scaling

Modern on-shell S-matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for General Relativity still rely on off-shell Feynman diagram analysis. Here, we complete the fully on-shell proof of Ref.~\cite{ST} that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to General Relativity tree amplitudes. We do so by showing that the surprising requirement of "bonus" $z^{-2}$ scaling under a BCFW shift directly follows from Bose-symmetry. Moreover, we show that amplitudes in generic theories subjected to BCFW deformations of identical particles necessarily scale as $z^{\rm even}$. When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under non-adjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as $z^{-4}$, compared to the $z^{-1}$ behavior for conformal Chern-Simons matter theory.

hep-th↗

arXiv2014

T-Reflection

We point out the presence of a $T \to -T$ temperature-reflection ($T$-reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of $T$-reflection symmetry in systems with exactly-calculable partition functions. We show that $T$-reflection symmetry is present in a variety of conformal and non-conformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under $T$-reflections. An interesting property of the $T$-reflection symmetry is that it can be broken by shifts of the vacuum energy.

hep-th↗

arXiv2014

Anomalies without an action

Modern on-shell methods allow us to construct both the classical and quantum S-matrix for a large class of theories, without utilizing knowledge of the interacting Lagrangian. It was recently shown that the same applies for chiral gauge theories, where the constraints from anomaly cancelation can be recast into the tension between unitarity and locality, without any reference to gauge symmetry. In this paper, we give a more detailed exploration, for chiral QED and QCD. We study the rational terms that are mandated by locality, and show that the factorization poles of such terms reveal a new particle in the spectrum, the Green-Schwarz two-from. We further extend the analysis to six-dimensional gravity coupled to chiral matter, including self-dual two-forms for which covariant actions generically do not exist. Despite this, the on-shell methods define the correct quantum S-matrix by demonstrating that locality of the one-loop amplitude requires combination of chiral matter that is consistent with that of anomaly cancelation.

hep-th↗

arXiv2012

One-loop renormalization and the S-matrix

In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the bubble coefficients captures the 1-loop UV behavior. In particular, in a renormalizable theory the sum of the bubble coefficients equals the tree-level amplitude times a proportionality constant that is related to the one-loop beta function coefficient beta_0. In this paper, we study how this proportionality is achieved from the viewpoint of on-shell amplitudes. For n-point MHV amplitude in (super) Yang-Mills theory, we demonstrate the existence of a hidden structure in each individual bubble coefficient which directly leads to systematic cancellations within the sum of them. The origin of this structure can be attributed to the collinear poles within a two-particle cut. Due to the cancellation, the one-loop beta function coefficient can be identified as a sum over the residues of unique collinear poles in particular two-particle cuts. Using CSW recursion relations, we verify the generality of this statement by reproducing the correct proportionality factor from such cuts for n-point split-helicity N^kMHV amplitudes.

hep-th↗