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Superpotential
About: Superpotential is a research topic. Over the lifetime, 3836 publications have been published within this topic receiving 137867 citations.
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TL;DR: In this paper, it was shown that the conformally invariant (3, 4, 1 ) superpotential is generated by the Fayet-Iliopoulos term of the gauge superfield.
99 citations
TL;DR: In this paper, it was shown that the nonperturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator.
Abstract: The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated vector bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the vector bundle moduli. This method is illustrated by a number of non-trivial examples.
99 citations
TL;DR: In this article, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory.
Abstract: We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.
99 citations
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TL;DR: In this article, a systematic investigation of the space of 2+1 dimensional quiver gauge theories is initiated, with a succinct forward algorithm, and the authors show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data.
Abstract: We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly different theories, we see a new emergence of "toric duality".
98 citations
TL;DR: In this paper, the authors explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau three-fold.
Abstract: We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau three- folds. The domainwall tension is identified with a Poincare normal func- tion — a transversal holomorphic section of the Griffiths intermediate Jacobian — via the Abel-Jacobi map. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.
98 citations