31 research outputs found
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.Comment: 17 pages: Minor corrections in text (due to a helpful referee),
updated affiliations. Accepted for publication in the International Journal
for Number Theory (IJNT
Spectral sum rules for confining large-N theories
We consider asymptotically-free four-dimensional large- gauge theories
with massive fermionic and bosonic adjoint matter fields, compactified on
squashed three-spheres, and examine their regularized large- 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 . Our
results motivate us to conjecture some universal spectral sum rules for these
large gauge theories.Comment: 25 pages, 2 figures. v2: fixed typos, added references, and some
minor improvements to discussio
Bose-Fermi Degeneracies in Large Adjoint QCD
We analyze the large limit of adjoint QCD, an gauge theory with
flavors of massless adjoint Majorana fermions, compactified on . We focus on the weakly-coupled confining small- regime. If
the fermions are given periodic boundary conditions on , 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 size , even though the bosonic and
fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in
the confining phase for any , explaining how it is able to enjoy
large volume independence for any . The large boson-fermion
cancellations take place in a setting where adjoint QCD is manifestly
non-supersymmetric at any finite , and are consistent with the recent
conjecture that adjoint QCD has emergent fermionic symmetries in the large
limit.Comment: 35 pages, 5 figures. v3: further minor correction
The chiral condensate in a constant electromagnetic field
We study the shift of the chiral condensate in a constant electromagnetic
field in the context of chiral perturbation theory. Using the Schwinger
proper-time formalism, we derive a one-loop expression correct to all orders in
. Our result correctly reproduces a previously derived
``low-energy theorem'' for . We show that it is essential to include
corrections due to non-vanishing in order for a low energy theorem to
have any approximate regime of validity in the physical universe. We generalize
these results to systems containing electric fields, and discuss the regime of
validity for the results. In particular, we discuss the circumstances in which
the method formally breaks down due to pair creation in an electric field.Comment: 9 pages, 6 figures, LaTeX; removed extraneous section + minor
revision