Title | Instanton counting on compact manifolds |

Publication Type | Thesis |

Year of Publication | 2016 |

Authors | Ronzani, M |

University | SISSA |

Keywords | Supersymmetry |

Abstract | In this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- |

URL | http://urania.sissa.it/xmlui/handle/1963/35219 |

Custom 1 | 35521 |

Custom 2 | Mathematics |

Custom 4 | 1 |

Custom 5 | MAT/07 |

Custom 6 | Submitted by mronzani@sissa.it (mronzani@sissa.it) on 2016-09-16T15:39:32Z |

## Instanton counting on compact manifolds

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