arXiv subjects

Sergei Gukov

Publications and source records attributed to Sergei Gukov.

At least 127 records · Page 7Linked to original sources

arXiv2003

Heterotic Moduli Stabilization with Fractional Chern-Simons Invariants

We show that fractional flux from Wilson lines can stabilize the moduli of heterotic string compactifications on Calabi-Yau threefolds. We observe that the Wilson lines used in GUT symmetry breaking naturally induce a fractional flux. When combined with a hidden-sector gaugino condensate, this generates a potential for the complex structure moduli, Kahler moduli, and dilaton. This potential has a supersymmetric AdS minimum at moderately weak coupling and large volume. Notably, the necessary ingredients for this construction are often present in realistic models. We explore the type IIA dual phenomenon, which involves Wilson lines in D6-branes wrapping a three-cycle in a Calabi-Yau, and comment on the nature of the fractional instantons which change the Chern-Simons invariant.

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arXiv2003

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial

We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the A-polynomial of a knot. Using this approach, we find some new and rather surprising relations between the A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic 3-manifolds. These relations generalize the volume conjecture and the Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between the SL(2,C) partition function and the colored Jones polynomial.

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arXiv2002

Perturbative Analysis of Gauged Matrix Models

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that non-perturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model/gauge theory (even though in some of these cases the exact answer can also be obtained by summing up planar diagrams of matrix models).

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arXiv2002

Rational Conformal Field Theories and Complex Multiplication

We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT's corresponding to T^2 target and identify the Cardy branes with geometric branes. The T^2's leading to RCFT's admit ``complex multiplication'' which characterizes Cardy branes as specific D0-branes. We propose a condition for the conformal sigma model to be RCFT for arbitrary Calabi-Yau n-folds, which agrees with the known cases. Together with recent conjectures by mathematicians it appears that rational conformal theories are not dense in the space of all conformal theories, and sometimes appear to be finite in number for Calabi-Yau n-folds for n>2. RCFT's on K3 may be dense. We speculate about the meaning of these special points in the moduli spaces of Calabi-Yau n-folds in connection with freezing geometric moduli.

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arXiv2002

Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds

We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP(2) bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping the 5-sphere. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G_2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first non-trivial example of a topology changing transition with only 1/16 supersymmetry.

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arXiv2002

IIA String Theory on Calabi-Yau Fourfolds with Background Fluxes

Looking for string vacua with fixed moduli, we study compactifications of type IIA string theory on Calabi-Yau fourfolds in the presence of generic Ramond-Ramond fields. We explicitly derive the (super)potential induced by Ramond-Ramond fluxes performing a Kaluza-Klein reduction of the ten-dimensional effective action. This can be conveniently achieved in a formulation of the massive type IIA supergravity where all Ramond-Ramond fields appear in a democratic way. The result agrees with the general formula for the superpotential written in terms of calibrations. We further notice that for generic Ramond-Ramond fluxes all geometric moduli are stabilized and one finds non-supersymmetric vacua at positive values of the scalar potential.

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arXiv2002

Duality and Fibrations on G_2 Manifolds

We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M5-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into this framework. To give some examples, we construct two non-compact manifolds with G_2 structures: one with a K3 fibration, and one with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of the latter solution gives abelian BPS monopoles in 3+1 dimensions.

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arXiv2002

D-Brane Probes of Special Holonomy Manifolds

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.

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arXiv2002

D-Brane Probes of G_2 Holonomy Manifolds

We describe how mirror symmetry of three-dimensional N=1 supersymmetric gauge theories can be used to determine the theory on the world-volume of a D2-brane probe of manifolds with G_2 holonomy. This is a much shortened companion paper to hep-th/0202126.

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arXiv2002

Supersymmetry, G-flux and Spin(7) manifolds

In this note we study warped compactifications of M-theory on manifolds of Spin(7) holonomy in the presence of background 4-form flux. The explicit form of the superpotential can be given in terms of the self -dual Cayley calibration on the Spin(7) manifold, in agreement with the general formula propsed in hep-th/9911011.

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arXiv2001

M-Theory on Spin(7) Manifolds

We study M-theory on two classes of manifolds of Spin(7) holonomy that are developing an isolated conical singularity. We construct explicitly a new class of Spin(7) manifolds and analyse in detail the topology of the corresponding classical spacetimes. We discover also an intricate interplay between various anomalies in M-theory, string theory, and gauge theory within these models, and in particular find a connection between half-integral G-fluxes in M-theory and Chern-Simons terms of the N=1, D=3 effective theory.

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arXiv2001

Superstrings in 2D Backgrounds with R-R Flux and New Extremal Black Holes

The hybrid formalism is used to quantize the superstring compactified to two-dimensional target-space in a manifestly spacetime supersymmetric manner. A quantizable sigma model action is then constructed for the Type II superstring in curved two-dimensional supergravity backgrounds which can include Ramond-Ramond flux. Such curved backgrounds include Calabi-Yau four-fold compactifications with Ramond-Ramond flux, and new extremal black hole solutions in two-dimensional dilaton supergravity theory. These black hole solutions are a natural generalization of the CGHS model and might be possible to describe using a supergroup version of the SL(2,R)/U(1) WZW model. We also study some dynamical aspects of the new black holes, such as formation and evaporation.

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arXiv2001

Solitons, Superpotentials and Calibrations

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general formula for the superpotential and justify it comparing the supersymmetry conditions in D=2 and D=10 supergravity theories. We also suggest a geometric interpretation to the supersymmetric index in the two-dimensional effective theory in terms of topological invariants of the Calabi-Yau four-fold, and estimate the asymptotic growth of these invariants from BTZ black hole entropy. Finally, we explicitly construct new supersymmetric vacua for Type IIA string theory compactification on a Calabi-Yau four-fold with Ramond-Ramond fluxes.

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arXiv2001

Gauge Theory at Large N and New G_2 Holonomy Metrics

We find a one-parameter family of new G_2 holonomy metrics and demonstrate that it can be extended to a two-parameter family. These metrics play an important role as the supergravity dual of the large $N$ limit of four dimensional supersymmetric Yang-Mills. We show that these G_2 holonomy metrics describe the M-theory lift of the supergravity solution describing a collection of D6-branes wrapping the supersymmetric three-cycle of the deformed conifold geometry for any value of the string coupling constant.

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arXiv2001

Domain Walls, Black Holes, and Supersymmetric Quantum Mechanics

Supersymmetric solutions, such as BPS domain walls or black holes, in four- and five-dimensional supergravity theories with eight supercharges can be described by effective quantum mechanics with a potential term. We show how properties of the latter theory can help us to learn about the physics of supersymmetric vacua and BPS solutions in these supergravity theories. The general approach is illustrated in a number of specific examples where scalar fields of matter multiplets take values in symmetric coset spaces.

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arXiv2000

The Hagedorn transition in non-commutative open string theory

The Hagedorn transition in non-commutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five spacetime dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the D-brane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated from the bound state.

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arXiv2000

Two Two-Dimensional Supergravity Theories from Calabi-Yau Four-Folds

We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi-Yau four-fold. In Type IIA and Type IIB cases, respectively, new superspace formulations of N=(2,2) and N=(0,4) dilaton supergravities are found and their coupling to matter multiplets is discussed.

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arXiv2000

Domain Walls and Superpotentials from M Theory on Calabi-Yau Three-Folds

Compactification of M theory in the presence of G-fluxes yields N=2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza-Klein reduction of the eleven-dimensional action on a Calabi-Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a ``running volume'' and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS_5 vacuum of the 5-dimensional supergravity.

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