Squashed toric manifolds and higher depth mock modular forms - Kölner UniversitätsPublikationsServer

Gupta, Rajesh Kumar, Murthy, Sameer ORCID: 0000-0001-8864-7439 and Nazaroglu, Caner ORCID: 0000-0001-8844-2441 (2019). Squashed toric manifolds and higher depth mock modular forms. J. High Energy Phys. (2). NEW YORK: SPRINGER. ISSN 1029-8479

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DOI:10.1007/JHEP02(2019)064

Abstract

Squashed toric sigma models are a class of sigma models whose target space is a toric manifold in which the torus fibration is squashed away from the fixed points so as to produce a neck-like region. The elliptic genera of squashed toric-Calabi-Yau manifolds are known to obey the modular transformation property of holomorphic Jacobi forms, but have an explicit non-holomorphic dependence on the modular parameter. The elliptic genus of the simplest one-dimensional example is known to be a mixed mock Jacobi form, but the precise automorphic nature for the general case remained to be understood. We show that these elliptic genera fall precisely into a class of functions called higher-depth mock modular forms that have been formulated recently in terms of indefinite theta series. We also compute a generalization of the elliptic genera of these models corresponding to an additional set of charges corresponding to the toric symmetries. Finally we speculate on some relations of the elliptic genera of squashed toric models with the Vafa-Witten partition functions of = 4 SYM theory on a,a(TM)(2).

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Gupta, Rajesh Kumar	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Murthy, Sameer	UNSPECIFIED	orcid.org/0000-0001-8864-7439	UNSPECIFIED
Nazaroglu, Caner	UNSPECIFIED	orcid.org/0000-0001-8844-2441	UNSPECIFIED