David A. McGady

The Schwinger mechanism and graphene

The Schwinger mechanism, the production of charged particle-antiparticle pairs in a macroscopic external electric field, is derived for 2+1-dimensional theories. The rate of pair production per unit area for four species of massless fermions, with charge q, in a constant electric field E is given by {pi}{sup -2}({Dirac_h}/2{pi}){sup -3/2}c-tilde{sup -1/2}(qE){sup 3/2} where c-tilde is the speed of light for the two-dimensional system. To the extent undoped graphene behaves like the quantum field-theoretic vacuum for massless fermions in 2+1 dimensions, the Schwinger mechanism should be testable experimentally. A possible experimental configuration for this is proposed. Effects due to deviations from this idealized picture of graphene are briefly considered. It is argued that with present day samples of graphene, tests of the Schwinger formula may be possible.

Casimir Energy of Confining Large N Gauge Theories

Four-dimensional asymptotically free large N gauge theories compactified on S(R)(3)×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 nonsupersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the S(3) Casimir energy. The N=∞ renormalized vacuum energy turns out to vanish in the class of theories we have examined. This matches an implication of a recently observed temperature-reflection symmetry of such systems.

Bose-Fermi degeneracies in large N adjoint QCD

A bstractWe analyze the large N limit of adjoint QCD, an SU(N) gauge theory with Nf flavors of massless adjoint Majorana fermions, compactified on S3 × S1. We focus on the weakly-coupled confining small-S3 regime. If the fermions are given periodic boundary conditions on S1, 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 S1 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 ∼ N0, 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.

Consistency Conditions for Gauge Theory S Matrices from Requirements of Generalized Unitarity

In the modern on-shell approach, the perturbative S-matrix is constructed iteratively using onshell building blocks with manifest unitarity. As only gauge invariant quantities enter in the intermediate steps, the notion of gauge anomaly is absent. In this letter, we rephrase the anomaly cancellation conditions in a purely on-shell language. We demonstrate that while the unitarity-methods automatically lead to a unitary S-matrix, the rational terms that are required to enforce locality, invariably give rise to inconsistent factorization channels in chiral theories. In four-dimensions, the absence of such inconsistencies implies the vanishing of the cubic Casimir of the gauge group. In six-dimensions, if the symmetric trace of four generators does not vanish, the rational term develops a factorization channel revealing a new particle in the spectrum: the two-form of the Green-Schwarz mechanism. Thus in the purely on-shell construction, the notion of gauge-anomaly is replaced by the difficulty to consistently impose locality on the unitary S-matrix.

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.

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.

Spectral sum rules for confining large-N theories

A bstractWe 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.

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

A bstractIn 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.

Recursion relations for graviton scattering amplitudes from Bose symmetry and bonus scaling laws

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. [1] 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 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. 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, compared to the z behavior for conformal Chern-Simons matter theory.