Search results for "moduli space"

showing 10 items of 45 documents

Non-extremal black holes of N = 2, d = 4 supergravity

2011

We propose a generic recipe for deforming extremal black holes into non-extremal black holes and we use it to find and study the non-extremal black-hole solutions of several N=2,d=4 supergravity models (SL(2,R)/U(1), CPn and STU with four charges). In all the cases considered, the non-extremal family of solutions smoothly interpolates between all the different extremal limits, supersymmetric and not supersymmetric. This fact can be used to find explicitly extremal non-supersymmetric solutions in the cases in which the attractor mechanism does not completely fix the values of the scalars on the event horizon and they still depend on the boundary conditions at spatial infinity. We compare (su…

High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsEvent horizonSupergravitySuperpotentialFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)General Relativity and Quantum CosmologyModuli spaceBlack holeCombinatoricsHigh Energy Physics::TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theory (hep-th)AttractorCentral chargeSymplectic geometryJournal of High Energy Physics
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TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS

1991

We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal G}$ of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces and introduce supersymmetric quantum mechanics actions modelling the Riemannian geometry of submersions and embeddings, relevant to the projections ${\cal A}\rightarrow {\cal A}/{\cal G}$ and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ respectively. We explain the relation between Donal…

High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsHigh Energy Physics::PhenomenologyFOS: Physical sciencesAstronomy and AstrophysicsGauge (firearms)Riemannian geometryDonaldson theoryTopologyAtomic and Molecular Physics and OpticsModuli spaceHigh Energy Physics::Theorysymbols.namesakeHigh Energy Physics - Theory (hep-th)Euler characteristicsymbolsSupersymmetric quantum mechanicsGauge theoryInternational Journal of Modern Physics A
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Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy

2021

We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves. Liu, Zhang, and Zhou conjectured that the full partition function of this Dubrovin--Frobenius manifold is a tau-function of the extended nonlinear Schr\"odinger hierarchy, an extension of a particular rational reduction of the Kadomtsev--Petviashvili hierarchy. We prove a version of their conjecture specializing the Givental--M…

High Energy Physics - TheoryPure mathematicsRank (linear algebra)FOS: Physical sciences[MATH] Mathematics [math]01 natural sciencesCatalan numberMathematics::Algebraic Geometry[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]KP hierarchy0103 physical sciences[NLIN] Nonlinear Sciences [physics][NLIN]Nonlinear Sciences [physics][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]0101 mathematics[MATH]Mathematics [math]Mathematics::Symplectic GeometryMathematical PhysicsMathematicsHirota equationsPartition function (quantum field theory)ConjectureNonlinear Sciences - Exactly Solvable and Integrable SystemsHierarchy (mathematics)010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Statistical and Nonlinear PhysicsMathematical Physics (math-ph)16. Peace & justiceLax equationsManifoldModuli spaceMonotone polygonNonlinear Sciences::Exactly Solvable and Integrable SystemsHigh Energy Physics - Theory (hep-th)010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Exactly Solvable and Integrable Systems (nlin.SI)Catalan numbersFrobenius manifoldsLetters in Mathematical Physics
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On Hodge theory for the generalized geometry (I)

2013

Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.

Hodge theoryHolomorphic functionGeneral Physics and AstronomyComplex differential formGeometryKähler manifoldModuli spaceMathematics::Algebraic GeometryMathematics::Differential GeometryGeometry and TopologyComplex manifoldHodge dualMathematics::Symplectic GeometryMathematical PhysicsHodge structureMathematicsJournal of Geometry and Physics
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MR 2944715 Reviewed Zhu S. On the recursion formula for double Hurwitz numbers. Proceedings of the American Mathematical Society (2012) 140, no. 11, …

2013

Let $\mu = (\mu_{1}, \mu_{2}, \ldots, \mu_{m})$ and $\nu = (\nu_{1}, \nu_{2}, \ldots, \nu_{n})$ be two partitions of a positive integer $d$. In this paper, the author considers degree $d$ branched coverings of $\mathbb{P}^{1}$ with at most two special points, $0$ and $\infty$. Specifically, the purpose of the author is to give a recursion formula for double Hurwitz numbers $H^{g}_{\mu, \nu}$ by the cut-join analysis. Here, $H^{g}_{\mu, \nu}$ denotes the number of genus $g$ branched covers of $\mathbb{P}^{1}$ with branching date corresponding to $\mu$ and $\nu$ over $0$ and $\infty$, respectively. Furthemore, as application, the author gets a polynomial identity for linear Goulden-Jackson-Va…

Hurwitz numbers moduli space cut-join recursionSettore MAT/03 - Geometria
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Blown-up toric surfaces with non-polyhedral effective cone

2020

We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone, both in characteristic $0$ and in every prime characteristic $p$. As a consequence, we prove that the pseudo-effective cone of the Grothendieck-Knudsen moduli space $\overline M_{0,n}$ of stable rational curves is not polyhedral for $n\geq 10$ in characteristic $0$ and in characteristic $p$, for all primes $p$. Many of these toric surfaces are related to a very interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order. Their analysis in characteristic $p$ relies on tools of arithmetic geometry and Galois representations in …

Mathematics - Algebraic GeometryMathematics::Algebraic GeometryMathematics - Number TheoryEffective cones toric surfaces blow up moduli space.Applied MathematicsGeneral MathematicsFOS: MathematicsSettore MAT/03 - GeometriaNumber Theory (math.NT)Algebraic Geometry (math.AG)14C20 14M25 14E30 14H10 14H52
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Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces

2005

We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of this function and compute the signature of the Hessian at these points. The curve with the maximal number of automorphisms (the Burnside curve) turns out to be the point of the absolute maximum. Our results agree with the mass formula for orbifold Euler characteristics of the moduli space. A similar analysis is performed for the Bolza's strata of symmetric Riemann surfaces of genus two.

Mathematics(all)General MathematicsRiemann surface010102 general mathematicsMathematical analysis01 natural sciencesModuli spaceRiemann–Hurwitz formulaModuli of algebraic curvesRiemann Xi functionMathematics - Spectral Theorysymbols.namesakeRiemann problemMathematics::Algebraic GeometryGenus (mathematics)0103 physical sciencesFOS: Mathematicssymbols14H15010307 mathematical physics0101 mathematicsSpectral Theory (math.SP)Bergman metricMathematicsMathematische Zeitschrift
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Variations on S-fold CFTs

2019

A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of superconformal field theories, known as the S-fold CFTs. Previously it has been proposed that the corresponding quiver theory has a link involving the T(U(N)) theory. In this paper, we generalise the preceding result by studying quivers that contain a T(G) link, where G is self-dual under S-duality. In particular, the cases of G = SO(2N), USp'(2N) and G_2 are examined in detail. We propose the theories that arise from an appropriate insertion of an S-fold into a brane system, in the presence of an orientifold threeplane or an orientifold fiveplane. By analysing the moduli spaces, we test…

PhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsPure mathematicsClass (set theory)Settore FIS/02 - Fisica Teorica Modelli E Metodi Matematici010308 nuclear & particles physicsQuiverFOS: Physical sciencesField (mathematics)01 natural sciencesSupersymmetric Gauge TheoryModuli spaceHigh Energy Physics - Theory (hep-th)Orientifold0103 physical sciencesSupersymmetry and Dualitylcsh:QC770-798lcsh:Nuclear and particle physics. Atomic energy. RadioactivityBrane010306 general physicsMirror symmetryLink (knot theory)Duality in Gauge Field TheoriesDuality in Gauge Field Theories Supersymmetric Gauge Theory Supersymmetry and Duality
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No-scale N=4 supergravity coupled to Yang-Mills: the scalar potential and super-Higgs effect

2002

We derive the scalar potential of the effective theory of type IIB orientifold with 3-form fluxes turned on in presence of non abelian brane coordinates. N=4 supergravity predicts a positive semidefinite potential with vanishing cosmological constant in the vacuum of commuting coordinates, with a classical moduli space given by three radial moduli and three RR scalars which complete three copies of the coset (U(1,1+n)/U(1)\otimes U(1+n)), together with 6n D3-branes coordinates, n being the rank of the gauge group G. Implications for the super Higgs mechanism are also discussed.

PhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsSupergravityFísicaModuli spaceModulisymbols.namesakeGeneral Relativity and Quantum CosmologyHigh Energy Physics::TheoryOrientifoldGauge groupHiggs bosonsymbolsBraneHiggs mechanismParticle Physics - TheoryMathematical physics
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Equivariance in topological gravity

1992

Abstract We present models of topological gravity for a variety of moduli space conditions. In four dimensions, we construct a model for self-dual gravity characterized by the moduli condition R + μν =0, and in two dimensions we treat the case of constant scalar curvature. Details are also given for both flat and Yang-Mills type moduli conditions in arbitrary dimensions. All models are based on the same fundamental multiplet which conveniently affords the construction of a complete hierarchy of observables. This approach is founded on a symmetry algebra which includes a local vector supersymmetry, in addition to a global BRST-like symmetry which is equivariant with respect to Lorentz transf…

PhysicsModuli of algebraic curvesHigh Energy Physics::TheoryNuclear and High Energy PhysicsModular equationEquivariant mapQuantum gravityInvariant (mathematics)TopologyMultipletGeneral Theoretical PhysicsModuliModuli space
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