Abstract
Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.
Highlights
We will refer the two types of constructions as the A-type and the B-type
In a prototypical example [1] of an A-type construction, d = 1 and the two-dimensional theory on I × M1 is the A-model [31], which may be obtained from two-dimensional N = (2, 2) supersymmetric sigma model by the A-twist
One way to do so is to embed them into string theory using branes. This approach proves to be fruitful, as it allows one to exploit the rich structure of dualities in string theory [10, 30]. It seems that a large class of bosonic gauge theories with holomorphic action functionals and complex gauge groups admit A-type and B-type constructions, at least formally, since they can always be reformulated as zero-dimensional gauged sigma models
Summary
In the examples with d = 3, 4 described above, d-dimensional Chern-Simons theory is realized by (d+1)- and (d+2)-dimensional maximally supersymmetric Yang-Mills theories This pattern continues to hold for d = 5, 6, and we will explain the A-type and B-type constructions in these cases. This approach proves to be fruitful, as it allows one to exploit the rich structure of dualities in string theory [10, 30] It seems that a large class of bosonic gauge theories with holomorphic action functionals and complex gauge groups admit A-type and B-type constructions, at least formally, since they can always be reformulated as zero-dimensional gauged sigma models. We will explain how to construct good boundary conditions using a gradient flow
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