arXiv subjects

Roberto Zucchini

Publications and source records attributed to Roberto Zucchini.

At least 37 records · Page 2Linked to original sources

arXiv2011

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.

hep-th↗

arXiv2010

The gauging of BV algebras

A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0 ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1 ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher $N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.

hep-th↗

arXiv2008

The Lie algebroid Poisson sigma model

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory and the gauged A topological sigma model. In this paper, generalizing the above construction, we construct the Lie algebroid Poisson sigma model. This is yielded by gauging a Hamiltonian Lie groupoid symmetry of the Poisson sigma model target space. We use the BV quantization approach in the AKSZ geometrical version to ensure consistent quantization and target space covariance. The model has an extremely rich geometry and an intricate BV cohomology, which are studied in detail.

math-ph↗

arXiv2008

Gauging the Poisson sigma model

We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.

hep-th↗

arXiv2007

The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction

We revisit our earlier work on the AKSZ formulation of topological sigma model on generalized complex manifolds, or Hitchin model. We show that the target space geometry geometry implied by the BV master equations is Poisson--quasi--Nijenhuis geometry recently introduced and studied by Stiénon and Xu (in the untwisted case). Poisson--quasi--Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case. Next, we show how gauging and reduction can be implemented in the Hitchin model. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman, suggesting a natural framework for the study of reduction of Poisson--quasi--Nijenhuis manifolds.

hep-th↗

arXiv2006

BiHermitian Supersymmetric Quantum Mechanics

BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.

hep-th↗

arXiv2006

The biHermitian topological sigma model

BiHermitian geometry, discovered long ago by Gates, Hull and Roceck, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we work out the type A and B topological sigma models for a general biHermtian target space, we write down the explicit expression of the sigma model's action and BRST transformations and present a computation of the topological gauge fermion and the topological action.

hep-th↗

arXiv2005

A topological sigma model of biKaehler geometry

BiKaehler geometry is characterized by a Riemannian metric g_{ab} and two covariantly constant generally non commuting complex structures K_+^a_b, K_-^a_b, with respect to which g_{ab} is Hermitian. It is a particular case of the biHermitian geometry of Gates, Hull and Roceck, the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. We present a sigma model for biKaehler geometry that is topological in the following sense: i) the action is invariant under a fermionic symmetry delta; ii) delta is nilpotent on shell; iii) the action is delta--exact on shell up to a topological term; iv) the resulting field theory depends only on a subset of the target space geometrical data. The biKaehler sigma model is obtainable by gauge fixing the Hitchin model with generalized Kaehler target space. It further contains the customary A topological sigma model as a particular case. However, it is not seemingly related to the (2,2) supersymmetric biKaehler sigma model by twisting in general.

hep-th↗

arXiv2005

Generalized complex geometry, generalized branes and the Hitchin sigma model

Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin--Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.

hep-th↗

arXiv2004

A sigma model field theoretic realization of Hitchin's generalized complex geometry

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.

hep-th↗

arXiv2004

Global Aspects of Abelian and Center Projections in SU(2) Gauge Theory

We show that the global aspects of Abelian and center projection of a SU(2) gauge theory on an arbitrary manifold are naturally described in terms of smooth Deligne cohomology. This is achieved through the introduction of a novel type of differential topological structure, called Cho structure. Half integral monopole charges appear naturally in this framework.

hep-th↗

arXiv2004

Abelian Duality and Abelian Wilson Loops

We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.

hep-th↗

arXiv2004

Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory

Recently, Witten showed that there is a natural action of the group SL(2,Z) on the space of 3 dimensional conformal field theories with U(1) global symmetry and a chosen coupling of the symmetry current to a background gauge field on a 3-fold N. He further argued that, for a class of conformal field theories, in the nearly Gaussian limit, this SL(2,Z) action may be viewed as a holographic image of the well-known SL(2,Z) Abelian duality of a pure U(1) gauge theory on AdS-like 4-folds M bounded by N, as dictated by the AdS/CFT correspondence. However, he showed that explicitly only for the generator T; for the generator S, instead, his analysis remained conjectural. In this paper, we propose a solution of this problem. We derive a general holographic formula for the nearly Gaussian generating functional of the correlators of the symmetry current and, using this, we show that Witten's conjecture is indeed correct when N=S^3. We further identify a class of homology 3-spheres N for which Witten's conjecture takes a particular simple form.

hep-th↗

arXiv2002

Relative Topological Integrals and Relative Cheeger-Simons Differential Characters

Topological integrals appear frequently in Lagrangian field theories. On manifolds without boundary, they can be treated in the framework of (absolute) (co)homology using the formalism of Cheeger--Simons differential characters. String and D--brane theory involve field theoretic models on worldvolumes with boundary. On manifolds with boundary, the proper treatment of topological integrals requires a generalization of the usual differential topological set up and leads naturally to relative (co)homology and relative Cheeger--Simons differential characters. In this paper, we present a construction of relative Cheeger--Simons differential characters which is computable in principle and which contains the ordinary Cheeger--Simons differential characters as a particular case.

hep-th↗

arXiv2002

Target Space Equivariant Cohomological Structure of the Poisson Sigma Model

We study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite dimensional Lie algebra. We show that the structure of the action and the properties of the gauge invariant observables can be understood in terms of the associated target space equivariant cohomology. We use a de Rham superfield formalism to efficiently explore the implications of the Batalin Vilkoviski master equation.

math-ph↗

arXiv2000

3-point functions of universal scalars in maximal SCFTs at large N

We compute all 3-point functions of the ``universal'' scalar operators contained in the interacting, maximally supersymmetric CFTs at large N by using the AdS/CFT correspondence. These SCFTs are related to the low energy description of M5, M2 and D3 branes, and the common set of universal scalars corresponds through the AdS/CFT relation to the fluctuations of the metric and the magnetic potential along the internal manifold. For the interacting (0,2) SCFT_6 at large N, which is related to M5 branes, this set of scalars is complete, while additional non-universal scalar operators are present in the d=4, N=4 super Yang-Mills theory and in the N=8 SCFT_3, related to D3 and M2 branes, respectively.

hep-th↗

arXiv1999

Three Point Functions for a Class of Chiral Operators in Maximally Supersymmetric CFT at Large N

We present a calculation of three point functions for a class of chiral operators, including the primary ones, in d = 3, N = 8; d = 6, N = (2,0) and d = 4, N = 4 superconformal field theories at large N. These theories are related to the infrared world-volume descriptions of N coincident M2, M5 and D3 branes, respectively. The calculation is done in the framework of the AdS/CFT correspondence and can be given a unified treatment employing a gravitational action in arbitrary dimensions D, coupled to a p+1 form and suitably compactified on AdS(D-2-p) x S(2+p). The interesting cases are obtained setting (D,p) to the values (11,5), (11,2) and (10,3).

hep-th↗

arXiv1999

Three Point Functions of Chiral Primary Operators in d=3, N= 8 and d=6, N=(2,0) SCFT at Large N

We use the AdS/CFT correspondence to calculate three point functions of chiral primary operators at large N in d=3, N=8 and d=6, N=(2,0) superconformal field theories. These theories are related to the infrared fixed points of world-volume descriptions of N coincident M2 and M5 branes, respectively. The computation can be generalized by employing a gravitational action in arbitrary dimensions D, coupled to a (p+1)-form and appropriately compactified on AdS(D-p-2)xS(p+2). We note a surprising coincidence: this generalized model reproduces for D=10, p=3 the three point functions of d=4, N=4 SYM chiral primary operators at large N.

hep-th↗