ST1 - Branes and Instantons in String Theory |
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Speaker |
Billo', Marco |
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Coauthors |
Frau, Marialuisa; Fucito, Francesco; Lerda, Alberto; Morales, Jose F. |
| Talk Title |
Resumming Instantons in N=2* Theories with ABCDE Gauge Groups |
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Abstract |
The pre-potential of 4d gauge theories with N=2 susy and an adjoint hypermultiplet of mass M (N=2* theories) has been shown to satisfy, for U(N) gauge groups, recursion relations among the coefficients h_n of its M expansion. These recursion relations are equivalent to the modular (or holomorphic) anomaly for the partition function, which is well understood in a topological string setting, and allow to write the said coefficients in terms of (quasi)-modular forms of the instanton weight $q$, resumming thus the instanton contributions. By re-expressing the recursion relations in terms of roots of the gauge group, we are able to show that they can naturally be extended to all classical groups, as well as to E6,E7 and E8. In this way we propose exact expressions for the first terms in the mass expansion of the prepotential valid for all groups. At the one-istanton level, we propose a formula encompassing all terms in the mass expansion. We check our proposals against explicit computations of the prepotential from the Nekrasov approach, some of which had not yet been performed in the literature, finding full agreement. Epsilon-deformations can also be accomodated. |
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