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Modularity, and its consequences, in certain non-supersymmetric four-dimensional gauge theories
In this talk, I will discuss recently discovered emergent symmetries
within a calculable limit of four-dimensional gauge theories. The
particular limit is that of large N gauge theories, with arbitrary
numbers of massless adjoint fermions and scalars, placed on the
compact manifold S3 x S1, at weak-coupling. In this limit, we show
that the grand canonical partition functions have well-defined modular
weight. Modularity, easily and powerfully implies (a) these theories
behave like two-dimensional (irrational) conformal field theories, (b)
very general sum-rules for vacuum energies, and (c) a level-matching
between bosons and fermions, manifestly distinct from supersymmetry.
Whether these symmetries are evocative of integrability is not yet
clear. Time permitting, I will discuss moving away from this simplest
[Note: Theory Working Group 30+30 minute format]