Point-like bounding chains in open Gromov–Witten theory

On the polynomiality of orbifold Gromov–Witten theory of root stacks

Mathematische Zeitschrift ◽

10.1007/s00209-021-02782-y ◽

2021 ◽

Author(s):

Hsian-Hua Tseng ◽

Fenglong You

Keyword(s):

Witten Theory

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Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

Forum of Mathematics Pi ◽

10.1017/fmp.2021.3 ◽

2021 ◽

Vol 9 ◽

Author(s):

Pierrick Bousseau ◽

Honglu Fan ◽

Shuai Guo ◽

Longting Wu

Keyword(s):

Elliptic Curve ◽

Moduli Spaces ◽

Topological String ◽

Holomorphic Anomaly ◽

Holomorphic Anomaly Equation ◽

Anomaly Equation ◽

Witten Theory ◽

Generating Series ◽

Maximal Contact ◽

Higher Genus

Abstract We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

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Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

Journal of High Energy Physics ◽

10.1007/jhep09(2020)133 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Guido Festuccia ◽

Anastasios Gorantis ◽

Antonio Pittelli ◽

Konstantina Polydorou ◽

Lorenzo Ruggeri

Keyword(s):

Vector Field ◽

Extended Supersymmetry ◽

General Framework ◽

Gauge Theories ◽

Killing Vector ◽

Killing Vector Field ◽

Explicit Result ◽

Yang Mills ◽

Self Duality ◽

Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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Testing Seiberg–Witten theory to all orders in the instanton expansion

Nuclear Physics B ◽

10.1016/s0550-3213(02)00558-8 ◽

2002 ◽

Vol 639 (1-2) ◽

pp. 66-94 ◽

Cited By ~ 17

Author(s):

Timothy J. Hollowood

Keyword(s):

Witten Theory

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TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x91001738 ◽

1991 ◽

Vol 06 (20) ◽

pp. 3571-3598 ◽

Cited By ~ 1

Author(s):

NOUREDDINE CHAIR ◽

CHUAN-JIE ZHU

Keyword(s):

Field Theory ◽

Topological Field Theory ◽

Fundamental Representation ◽

Conformal Blocks ◽

Conformal Field ◽

Witten Theory ◽

Topological Field ◽

General Program ◽

The One ◽

Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

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