BPS invariants of $\CN=4$ gauge theory on Hirzebruch surfaces

Manschot, Jan

doi:10.4310/cntp.2012.v6.n2.a4

Cited by 33 publications

(54 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This gives further evidence for such a factorization to hold for generic N [5,8], in which case the Z N would involve (N − 1)-dimensional iterated integrals of modular forms, and consequently mock modular forms of depth N − 1. These functions will equally play a role for other four-manifolds with b + 2 = 1 [8,9]. Mock modular forms of higher depth have appeared in a few other instances, i.e.…”

Section: )mentioning

confidence: 97%

Vafa–Witten Theory and Iterated Integrals of Modular Forms

Manschot

2019

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

Vafa-Witten (VW) theory is a topologically twisted version of N = 4 supersymmetric Yang-Mills theory. S-duality suggests that the partition function of VW theory with gauge group SU (N ) transforms as a modular form under duality transformations. Interestingly, Vafa and Witten demonstrated the presence of a modular anomaly, when the theory has gauge group SU (2) and is considered on the complex projective plane P 2 . This modular anomaly could be expressed as an integral of a modular form, and also be traded for a holomorphic anomaly. We demonstrate that the modular anomaly for gauge group SU (3) involves an iterated integral of modular forms. Moreover, the modular anomaly for SU (3) can be traded for a holomorphic anomaly, which is shown to factor into a product of the partition functions for lower rank gauge groups. The SU (3) partition function is mathematically an example of a mock modular form of depth two.

show abstract

Section: )mentioning

confidence: 97%

Vafa–Witten Theory and Iterated Integrals of Modular Forms

Manschot

2019

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For such line bundles over rational surfaces, the DT invariants Ω(γ; z a ) with p 0 = 0 can be computed explicitly [68], and the analogue of the MSW CFT is a (0,4)-supersymmetric sigma model with target space given by the Atiyah-Hitchin moduli space of monopoles in three dimensions [45,69]. An important difference between the rigid case and the assumptions in this paper is that the generating function h p,µ (τ ) of DT invariants for rational surfaces is mock modular [66,70]. It is natural to expect that its non-holomorphic modular completion will arise from multi-instanton corrections.…”

Section: Jhep04(2013)002mentioning

confidence: 99%

D3-instantons, mock theta series and twistors

Alexandrov

Manschot

Pioline

2013

J. High Energ. Phys.

Self Cite

101

View full text Add to dashboard Cite

The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

show abstract

“…Within the framework of geometric engineering the strings are realized as M5 branes wrapping a four-cycle in a non-compact Calabi-Yau threefold and the elliptic genus of the strings gets related to the partition function of twisted N = 4 SYM on the four-manifold [6]. Such partition functions are mathematically generating functions of sheaves on algebraic surfaces, and recently there has been a lot of progress in obtaining them [7][8][9][10]. Such sheaf counting can then be…”

Section: Introductionmentioning

confidence: 99%