### Abstract

We study strong-weak coupling duality (S-duality) in N = 4 supersymmetric non-Abelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using 't Hooft's prescription, i.e. through functional integrals at finite volume in the presence of twisted boundary conditions. Then, we find those free energies in two limiting cases: small and large coupling constant. Finally, we extend the free energies to all values of the coupling constant (and the theta angle) by presenting a fully S-duality invariant ansatz. This ansatz obeys all relevant consistency conditions; in particular, it obeys 't Hooft duality equations and Witten's magnetic-electric transmutation. The existence of an S-duality invariant, consistent definition of free energies supports the claim made in the literature that S-duality is a duality symmetry of N = 4 SUSY Yang-Mills. Our ansatz also suggests that N = 4, irrespective of whether partially broken or not, is in a self-dual phase: no phase transitions occur between the strong and weak coupling regimes.

Original language | English (US) |
---|---|

Pages (from-to) | 331-338 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 334 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 18 1994 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*334*(3-4), 331-338. https://doi.org/10.1016/0370-2693(94)90697-1

**Non-Abelian strong-weak coupling duality in (string-derived) N=4 supersymmetric Yang-Mills theories.** / Girardello, Luciano; Giveon, Amit; Porrati, Massimo; Zaffaroni, Alberto.

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 334, no. 3-4, pp. 331-338. https://doi.org/10.1016/0370-2693(94)90697-1

}

TY - JOUR

T1 - Non-Abelian strong-weak coupling duality in (string-derived) N=4 supersymmetric Yang-Mills theories

AU - Girardello, Luciano

AU - Giveon, Amit

AU - Porrati, Massimo

AU - Zaffaroni, Alberto

PY - 1994/8/18

Y1 - 1994/8/18

N2 - We study strong-weak coupling duality (S-duality) in N = 4 supersymmetric non-Abelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using 't Hooft's prescription, i.e. through functional integrals at finite volume in the presence of twisted boundary conditions. Then, we find those free energies in two limiting cases: small and large coupling constant. Finally, we extend the free energies to all values of the coupling constant (and the theta angle) by presenting a fully S-duality invariant ansatz. This ansatz obeys all relevant consistency conditions; in particular, it obeys 't Hooft duality equations and Witten's magnetic-electric transmutation. The existence of an S-duality invariant, consistent definition of free energies supports the claim made in the literature that S-duality is a duality symmetry of N = 4 SUSY Yang-Mills. Our ansatz also suggests that N = 4, irrespective of whether partially broken or not, is in a self-dual phase: no phase transitions occur between the strong and weak coupling regimes.

AB - We study strong-weak coupling duality (S-duality) in N = 4 supersymmetric non-Abelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using 't Hooft's prescription, i.e. through functional integrals at finite volume in the presence of twisted boundary conditions. Then, we find those free energies in two limiting cases: small and large coupling constant. Finally, we extend the free energies to all values of the coupling constant (and the theta angle) by presenting a fully S-duality invariant ansatz. This ansatz obeys all relevant consistency conditions; in particular, it obeys 't Hooft duality equations and Witten's magnetic-electric transmutation. The existence of an S-duality invariant, consistent definition of free energies supports the claim made in the literature that S-duality is a duality symmetry of N = 4 SUSY Yang-Mills. Our ansatz also suggests that N = 4, irrespective of whether partially broken or not, is in a self-dual phase: no phase transitions occur between the strong and weak coupling regimes.

UR - http://www.scopus.com/inward/record.url?scp=0043009793&partnerID=8YFLogxK

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U2 - 10.1016/0370-2693(94)90697-1

DO - 10.1016/0370-2693(94)90697-1

M3 - Article

VL - 334

SP - 331

EP - 338

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -