Superpotential

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

A barren landscape?—Metastable de Sitter vacua are nongeneric in string theory

Abstract: We consider the generation of a nonperturbative superpotential in F-theory compactifications with flux. We derive a necessary condition for the generation of such a superpotential in F theory. For models with a single volume modulus, we show that the volume modulus is never stabilized by either Abelian instantons or gaugino condensation. We then comment on how our analysis extends to a larger class of compactifications. From our results, it appears that among large volume string compactifications, metastable de Sitter vacua (should any exist) are nongeneric.

M5 brane and four dimensional N=1 theories I

Abstract: Four dimensional N=1 theories are engineered by compactifying six dimensional (2,0) theory on a Riemann surface with regular punctures. A generalized Hitchin's equation involving two Higgs fields is proposed as the BPS equation for N=1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing N=2 puncture. As an application, we show that the Seiberg duality of SU(N) SQCD with Nf=2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and also find four more dual theories.

Supersymmetric quantum mechanics and large-N expansions.

Abstract: Supersymmetric quantum mechanics is formulated for spherically symmetric potentials in N spatial dimensions. It is seen that the supersymmetric partner potential of a given potential can be effectively treated as being in N+2 dimensions. This fact is exploited in calculations using the shifted 1/N expansion. Also, the violation of the no-degeneracy theorem in one dimension by the Coulomb potential is seen as a consequence of this result.

Saltatory de Sitter string vacua

Abstract: We extend a recent scenario of Kachru, Kallosh, Linde and Trivedi to fix the string moduli fields by using a combination of fluxes and non-perturbative superpotentials, leading to de Sitter vacua. In our scenario the non-perturbative superpotential is taken to be either, the racetrack scenario or the = 1* superpotential for an SU(N) theory, originally computed by Dorey and recently rederived using the techniques of Dijkgraaf-Vafa. The fact that this superpotential includes the full instanton contribution gives rise to the existence of a large number of minima, increasing with N. In the absence of supersymmetry breaking these correspond to supersymmetric anti de Sitter vacua. The introduction of antibranes lifts the minima to a chain of (non-supersymmetric) de Sitter minima with the value of the cosmological constant decreasing with increasing compactification scale. Surprisingly a similar picture occurs for the simpler system of the racetrack scenario. The relative semiclassical stability of these vacua is studied. Possible cosmological implications of these potentials are also discussed.

Reverse geometric engineering of singularities

Abstract: One can geometrically engineer supersymmetric field theories theories by placing D-branes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a non-commutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this non-commutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that D-branes probe. It is also argued that the identification of V is invariant under Seiberg dualities.