arXiv subjects

Martin Rocek

Publications and source records attributed to Martin Rocek.

At least 37 records · Page 2Linked to original sources

arXiv2006

A Gravitational Effective Action on a Finite Triangulation as a Discrete Model of Continuous Concepts

We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a triangulation. The variation of this function under local rescalings of the edge lengths sharing a vertex is the Euler density, and we use it to illustrate how continuous concepts can have natural discrete analogs.

hep-th↗

arXiv2006

Quaternion-Kahler spaces, hyperkahler cones, and the c-map

Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.

math.DG↗

arXiv2006

Ricci-flat supertwistor spaces

We show that supertwistor spaces constructed as a Kahler quotient of a hyperkahler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.

hep-th↗

arXiv2006

A Gravitational Effective Action on a Finite Triangulation

We construct a function of the edge-lengths of a triangulated surface whose variation under a rescaling of all the edges that meet at a vertex is the defect angle at that vertex. We interpret this function as a gravitational effective action on the triangulation, and the variation as a trace anomaly.

hep-th↗

arXiv2006

Generalized Kahler manifolds and off-shell supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.

hep-th↗

arXiv2005

Hypermultiplets and Topological Strings

The c-map relates classical hypermultiplet moduli spaces in compactifications of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces via a further compactification on a circle. We give an off-shell description of the c-map in N=2 superspace. The superspace Lagrangian for the hypermultiplets is a single function directly related to the prepotential of special geometry, and can therefore be computed using topological string theory. Similarly, a class of higher derivative terms for hypermultiplets can be computed from the higher genus topological string amplitudes. Our results provide a framework for studying quantum corrections to the hypermultiplet moduli space, as well as for understanding the black hole wave-function as a function of the hypermultiplet moduli.

hep-th↗

arXiv2005

Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N=(2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

hep-th↗

arXiv2004

On Calabi-Yau supermanifolds II

We study when Calabi-Yau supermanifolds M(1|2) with one complex bosonic coordinate and two complex fermionic coordinates are super Ricci-flat, and find that if the bosonic manifold is compact, it must have constant scalar curvature.

hep-th↗

arXiv2004

On Calabi-Yau supermanifolds

We prove that a Kahler supermetric on a supermanifold with one complex fermionic dimension admits a super Ricci-flat supermetric if and only if the bosonic metric has vanishing scalar curvature. As a corollary, it follows that Yau's theorem does not hold for supermanifolds.

hep-th↗

arXiv2004

Quivers, Quotients, and Duality

We give a direct computational proof of N=2 Seiberg duality for arbitrary quivers, and find the action on the Fayet-Iliopoulos parameters. We also find a new analogous classical duality for Kahler potentials of N=1 quivers that generalizes the trivial duality Gr(N,N+M) ~ Gr(M,N+M) for Grassmannians.

hep-th↗

arXiv2004

Quantum Corrections to the Universal Hypermultiplet and Superspace

We investigate quantum corrections to the effective action of the universal hypermultiplet in the language of projective superspace. We rederive the recently found one-loop correction to the universal hypermultiplet moduli space geometry. The deformed metric is described as a superspace action in terms of a single function, homogeneous of first degree. Our framework leads us to a natural proposal for the nonperturbative moduli space metric induced by five-brane instantons.

hep-th↗

arXiv2003

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.

hep-th↗

arXiv2003

Consistent Boundary Conditions for Open Strings

We study boundary conditions for the bosonic, spinning (NSR) and Green-Schwarz open string, as well as for 1+1 dimensional supergravity. We consider boundary conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or kappa(Siegel)-symmetry of the action, (3) closure of the set of boundary conditions under the symmetry transformations, and (4) the boundary limits of bulk Euler-Lagrange equations that are ``conjugate'' to other boundary conditions. We find corrections to Neumann boundary conditions in the presence of a bulk tachyon field. We discuss a boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of boundary conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neumann boundary conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.

hep-th↗

arXiv2002

Hyperkahler Cones and Orthogonal Wolf Spaces

We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. The geometry is completely encoded by a single function, the hyperkahler potential, which we compute from an SU(2) hyperkahler quotient of flat space. We derive the Killing vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone. For the non-compact case, the isometry group SO(n,4) contains n+2 abelian isometries which can be used to find a dual description in terms of n tensor multiplets and one double-tensor multiplet. Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space.

hep-th↗

arXiv2001

Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds

We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space. As an example of the general construction, we discuss the gauging and the corresponding scalar potential of hypermultiplets with the unitary Wolf spaces as target spaces. This class includes the universal hypermultiplet.

hep-th↗

arXiv2001

Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry

We study hyperkahler cones and their corresponding quaternion-Kahler spaces. We present a classification of 4(n-1)-dimensional quaternion-Kahler spaces with n abelian quaternionic isometries, based on dualizing superconformal tensor multiplets. These manifolds characterize the geometry of the hypermultiplet sector of perturbative moduli spaces of type-II strings compactified on a Calabi-Yau manifold. As an example of our construction, we study the universal hypermultiplet in detail, and give three inequivalent tensor multiplet descriptions. We also comment on the construction of quaternion-Kahler manifolds that may describe instanton corrections to the moduli space.

hep-th↗

arXiv2000

Non-commutative Soliton Scattering

We study solitons in three dimensional non-commutative scalar field theory at infinite non-commutativity parameter. We find the metric on the relative moduli space of all solitons of the form |n><n| and show that it is Kahler. We then find the geodesics of this metric and study the scattering of these solitons. In particular we find that the scattering is generally right angle for small values of the impact parameter. We can understand this behaviour in terms of a conical singularity at the origin of moduli space.

hep-th↗

arXiv1999

Hyperkahler quotients and algebraic curves

We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperkahler quotient of a linear space. We apply this method to four dimensional ALE spaces, and for the A_k, D_k, and E_6 cases, derive the explicit relation between the deformations of the curves away from the orbifold limit and the Fayet-Iliopoulos parameters in the corresponding quotient construction. We work out the orbifold limit of E_7, E_8, and some higher dimensional examples.

hep-th↗