Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A holomorphic anomaly in the elliptic genus   We consider a class of gauged linear sigma models (GLSMs) in two dimensions
that flow to non-compact (2,2) superconformal field theories in the infra-red,
a prototype of which is the SL(2,\IR)/U(1) (cigar) coset. We compute the
elliptic genus of the GLSMs as a path-integral on the torus using
supersymmetric localization. We find that the result is a Jacobi-like form that
is non-holomorphic in the modular parameter $\tau$ of the torus, with mock
modular behavior. This agrees with a previously-computed expression in the
cigar coset. We show that the lack of holomorphicity of the elliptic genus
arises from the contributions of a compact boson with momentum and winding
around the torus. This boson has an axionic shift symmetry and plays the role
of a compensator field that is needed to cancel the chiral anomaly in the rest
of the theory.

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con