Superpotential

About: Superpotential is a research topic. Over the lifetime, 3836 publications have been published within this topic receiving 137867 citations.

Bootstrapping SCFTs with Four Supercharges

Abstract: We study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension $2\leq d\leq 4$. We show how superconformal algebras with four Poincare supercharges can be treated in a formalism applicable to any, in principle continuous, value of $d$ and use this to construct the superconformal blocks for any $d\leq 4$. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the $d=2$, $\mathcal N=(2,2)$ minimal model with central charge $c=1$ and the theory of a free chiral multiplet in $d=4$, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.

Instanton induced open string superpotentials and branes at singularities

Abstract: We study different aspects of the non-perturbative superpotentials induced by Euclidean E3-branes on systems of D3/D7-branes located at Abelian orbifold singularities. We discuss in detail how the induced couplings are consistent with the U(1) symmetries carried by the D3/D7 branes. We construct different compact and non-compact examples, and show phenomenologically relevant couplings like μ-terms or certain Yukawa couplings generated by these E3 instantons. Some other novel effects are described. We show an example where E3 instantons combine with standard gauge instantons to yield new multi-instanton effects contributing to superpotential, along the lines of ref. [28]. In the case of non-SUSY ZN tachyon-free singularities it is shown how E3-instantons give rise to non perturbative scalar couplings including exponentially suppressed scalar bilinears.

D3 brane action and fermion zero modes in presence of background flux

Abstract: We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T6/Z2, twelve of the sixteen zero modes originally present are lifted by the flux.

Exact superpotentials for theories with flavors via a matrix integral

Abstract: We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of N = 1 theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential from surfaces with one boundary in the matrix integral. We compute exactly the effective superpotential for the case of the gauge group U(Nc), Nf massive flavor chiral multiplets in the fundamental and one massive chiral multiplet in the adjoint, together with a Yukawa coupling. We compare up to sixth order with the result obtained by standard field theory techniques in the already nontrivial case of Nc = 2 and Nf = 1. The agreement is perfect.

Gravitational Quantum Cohomology

Abstract: We discuss how the theory of quantum cohomology may be generalized to "gravitational quantum cohomology" by studying topological σ models coupled to two-dimensional gravity. We first consider σ models defined on a general Fano manifold M (manifold with a positive first Chern class) and derive new recursion relations for its two-point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus 0. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter t) is turned on and construct Lax operators (superpotentials) L whose residue integrals reproduce correlation functions. In the case of M = CPN the Lax operator is given by and agrees with the potential of the affine Toda theory of the AN type. We also obtain Lax operators for various Fano manifolds; Grassmannians, rational surfaces, etc. In these examples the number of variables of the Lax operators is the same as the dimension of the original manifold. Our result shows that Fano manifolds exhibit a new type of mirror phenomenon where mirror partner is a noncompact Calabi–Yau manifold of the type of an algebraic torus C*N equipped with a specific superpotential.