TY - JOUR

T1 - Equivariant elliptic cohomology, gauged sigma models, and discrete torsion

AU - Berwick-Evans, Daniel

N1 - Publisher Copyright:
© 2021 American Mathematical Society

PY - 2022

Y1 - 2022

N2 - For a finite group G, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background G-symmetry determine cocycles for complex analytic G-equivariant elliptic cohomology. Similar structures in supersymmetric mechanics determine cocycles for equivariant K-theory with complex coefficients. The path integral for gauge theory with a finite group constructs wrong-way maps associated to group homomorphisms. When applied to an inclusion of groups, we obtain the height 2 induced character formula of Hopkins, Kuhn, and Ravenel. For the homomorphism G → ∗, we recover Vafa’s gauging with discrete torsion. The image of equivariant Euler classes under gauging constructs modular form-valued invariants of representations that depend on a choice of string structure. We illustrate nontrivial dependence on the string structure for a 16-dimensional representation of the Klein 4-group.

AB - For a finite group G, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background G-symmetry determine cocycles for complex analytic G-equivariant elliptic cohomology. Similar structures in supersymmetric mechanics determine cocycles for equivariant K-theory with complex coefficients. The path integral for gauge theory with a finite group constructs wrong-way maps associated to group homomorphisms. When applied to an inclusion of groups, we obtain the height 2 induced character formula of Hopkins, Kuhn, and Ravenel. For the homomorphism G → ∗, we recover Vafa’s gauging with discrete torsion. The image of equivariant Euler classes under gauging constructs modular form-valued invariants of representations that depend on a choice of string structure. We illustrate nontrivial dependence on the string structure for a 16-dimensional representation of the Klein 4-group.

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U2 - 10.1090/tran/8527

DO - 10.1090/tran/8527

M3 - Article

AN - SCOPUS:85124624030

SN - 0002-9947

VL - 375

SP - 369

EP - 427

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -