Abstract
We show that the effective coupling constants τ of supersymmetric gauge theories described by hyperelliptic curves do not distinguish between the lattices of the two kinds of heterotic string. In particular, the following relation
holds. This is reminiscent of the relation, by T -duality, of the two heterotic strings. We suggest that such a relation extends to all curves describing effective supersymmetric gauge theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
G. Bonelli, M. Matone and M. Tonin, Solving N = 2 SYM by reflection symmetry of quantum vacua, Phys. Rev. D 55 (1997) 6466 [hep-th/9610026] [INSPIRE].
A. Klemm, W. Lerche, S. Yankielowicz and S. Theisen, Simple singularities and N = 2 supersymmetric Yang-Mills theory, Phys. Lett. B 344 (1995) 169 [hep-th/9411048] [INSPIRE].
P.C. Argyres and A.E. Faraggi, The vacuum structure and spectrum of N = 2 supersymmetric SU(N ) gauge theory, Phys. Rev. Lett. 74 (1995) 3931 [hep-th/9411057] [INSPIRE].
C. Poor, Schottky’s form for and the hyperelliptic locus, Proc. Amer. Math. Soc. 124 (1996) 1987.
J.-I. Igusa, Schottky’s invariant and quadratic forms, in E. B. Christoffel. The Influence of His Work on Mathematics and the Physical Sciences, Birkhäuser, Basel (1981), pp. 352-362, http://dx.doi.org/10.1007/978-3-0348-5452-8_24.
J.-I. Igusa, On the irreducibility of Schottky’s divisor, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981) 531.
D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, The Heterotic String, Phys. Rev. Lett. 54 (1985) 502 [INSPIRE].
D. Gaiotto, N=2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
S.K. Ashok, M. Billó, E. Dell’Aquila, M. Frau, R.R. John and A. Lerda, Non-perturbative studies of N = 2 conformal quiver gauge theories, Fortsch. Phys. 63 (2015) 259 [arXiv:1502.05581] [INSPIRE].
M. Matone, Instantons and recursion relations in N = 2 SUSY gauge theory, Phys. Lett. B 357 (1995) 342 [hep-th/9506102] [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [INSPIRE].
A. Marshakov, Tau-functions for Quiver Gauge Theories, JHEP 07 (2013) 068 [arXiv:1303.0753] [INSPIRE].
P. Gavrylenko and A. Marshakov, Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks, JHEP 05 (2014) 097 [arXiv:1312.6382] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
J.M. Isidro, On the WDVV equation and M-theory, Nucl. Phys. B 539 (1999) 379 [hep-th/9805051] [INSPIRE].
G. Bertoldi, S. Bolognesi, M. Matone, L. Mazzucato and Y. Nakayama, The Liouville geometry of N = 2 instantons and the moduli of punctured spheres, JHEP 05 (2004) 075 [hep-th/0405117] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
L.F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa and H. Verlinde, Loop and surface operators in N = 2 gauge theory and Liouville modular geometry, JHEP 01 (2010) 113 [arXiv:0909.0945] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1504.00349
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Matone, M. A surprising relation for the effective coupling constants of N = 2 super Yang-Mills theories. J. High Energ. Phys. 2015, 109 (2015). https://doi.org/10.1007/JHEP06(2015)109
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2015)109