Results 1  10
of
88
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
Abstract

Cited by 294 (26 self)
 Add to MetaCart
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke
Multiloop superstring amplitudes from nonminimal pure spinor formalism
"... Using the nonminimal version of the pure spinor formalism, manifestly superPoincaré covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picturechanging operators. The only subtlety comes from regularizing the functional integral over the ..."
Abstract

Cited by 52 (4 self)
 Add to MetaCart
(Show Context)
Using the nonminimal version of the pure spinor formalism, manifestly superPoincaré covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picturechanging operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRSTinvariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to tendimensional Fterms, i.e. terms in the tendimensional superspace action which do not involve integration over the maximum number of θ’s.
Lectures on curved betagamma systems, pure spinors, and anomalies
"... The curved betagamma system is the chiral sector of a certain infinite radius limit of the nonlinear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism an ..."
Abstract

Cited by 52 (3 self)
 Add to MetaCart
(Show Context)
The curved betagamma system is the chiral sector of a certain infinite radius limit of the nonlinear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism anomalies which we review. We analyze the curved betagamma system on the space of pure spinors, aiming to verify the consistency of Berkovits covariant superstring quantization. We demonstrate that under certain conditions both anomalies can be cancelled for the pure spinor sigma model, in which case one reproduces the old construction of B. Feigin and E. Frenkel.
Pure Spinor Formalism as an N=2 Topological String
, 2005
"... Following suggestions of Nekrasov and Siegel, a nonminimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ = 3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spinone generator, and the formalism is interpreted as a criti ..."
Abstract

Cited by 36 (7 self)
 Add to MetaCart
Following suggestions of Nekrasov and Siegel, a nonminimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ = 3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spinone generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the superPoincaré covariant computation of multiloop superstring amplitudes without picturechanging operators, the construction of a cubic open superstring field theory without contactterm problems, and a new fourdimensional version of the pure spinor formalism which computes Fterms in the spacetime action.
Topological heterotic rings
 Adv. Theor. Math. Phys
"... We prove the existence of topological rings in (0,2) theories containing nonanomalous leftmoving U(1) currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under nonsingular OPE which reduces to the (a,c) or (c,c) ring at (2,2) poi ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
(Show Context)
We prove the existence of topological rings in (0,2) theories containing nonanomalous leftmoving U(1) currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under nonsingular OPE which reduces to the (a,c) or (c,c) ring at (2,2) points and to a classical sheaf cohomology ring at large radius, defining a quantum sheaf cohomology away from these special loci. In the special case of CalabiYau compactifications, these rings are shown to exist globally on the moduli space if the rank of the holomorphic bundle is less than eight. June
Twodimensional twisted sigma models and the theory of chiral differential operators
, 2007
"... In this paper, we study the perturbative aspects of a twisted version of the twodimensional (0, 2) heterotic sigma model on a holomorphic gauge bundle E over a complex, hermitian manifold X. We show that the model can be naturally described in terms of the mathematical theory of “Chiral Differential ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
(Show Context)
In this paper, we study the perturbative aspects of a twisted version of the twodimensional (0, 2) heterotic sigma model on a holomorphic gauge bundle E over a complex, hermitian manifold X. We show that the model can be naturally described in terms of the mathematical theory of “Chiral Differential Operators”. In particular, the physical anomalies of the sigma model can be reinterpreted in terms of an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on X. One can also obtain a novel understanding of the sigma model oneloop beta function solely in terms of holomorphic data. At the (2, 2) locus, where the obstruction vanishes for any smooth manifold X, we obtain a purely mathematical description of the halftwisted variant of the topological Amodel and (if c1(X) = 0) its elliptic genus. By studying the halftwisted (2, 2) model on X = CP 1, one can show that a subset of the infinitedimensional space of physical operators generates an underlying superaffine Lie algebra. Furthermore, on a nonKähler, parallelised, group manifold with torsion, we uncover a direct relationship between the modulus of the corresponding sheaves of chiral de Rham complex, and the level of the underlying WZW theory.
Ambitwistor strings at null infinity and subleading soft limits
, 2014
"... The relationships between extended BMS symmetries at null infinity and Weinberg’s soft theorems for gravitons and photons together with their subleading generalizations are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified spac ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
(Show Context)
The relationships between extended BMS symmetries at null infinity and Weinberg’s soft theorems for gravitons and photons together with their subleading generalizations are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified spacetime. We show how it can be canonically identified with the cotangent bundle of null infinity. BMS symmetries of null infinity lift to give a hamiltonian action on ambitwistor space, both in general dimension and in its twistorial 4dimensional representation. General vertex operators arise from hamiltonians generating diffeomorphisms of ambitwistor space that determine the scattering from past to future null infinity. When a momentum eigenstate goes soft, the diffeomorphism defined by its leading and its subleading part are extended BMS generators realized in the world sheet conformal field theory of the ambitwistor string. More generally, this gives explicit perturbative correspondence between the scattering of null geodesics and that of the gravitational field via ambitwistor string theory.
Deformed quantum cohomology and (0,2) mirror symmetry
, 2007
"... We compute instanton corrections to correlators in the genuszero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P 1 × P 1, whose leftmoving fermions couple to a deformation of the tangent bundle. We then deduce the theory’s chiral ring from these corre ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
We compute instanton corrections to correlators in the genuszero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P 1 × P 1, whose leftmoving fermions couple to a deformation of the tangent bundle. We then deduce the theory’s chiral ring from these correlators, which reduces in the limit of zero deformation to the (2, 2) ring. Finally, we compare our results with the computations carried out by Adams et al.[ABS04] and Katz and Sharpe [KS06]. We find immediate agreement with the latter and an interesting puzzle in completely matching the chiral ring