Triangle Seminars

Abstract:
Localization is a non-perturbative method to exactly compute path integrals in supersymmetric theories. I will describe how localization can be thus used to test holographic duality in a non-conformal setting, namely for N=2* theory, which is a massive deformation of N=4 super Yang-Mills, and for which the dual supergravity background is known explicitly.

Abstract:
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinisation of the superalgebra gl (1|1): Its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.