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52
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 ..."
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Cited by 294 (26 self)
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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 ..."
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Cited by 52 (4 self)
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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.
Nongeometric Backgrounds and the First Order String Sigma Model
, 906
"... We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bivector, a twoform and an inverse metric. Lifting the topological sector of this action to three dimensions produces several WessZumino like terms which encode the ..."
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Cited by 28 (1 self)
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We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bivector, a twoform and an inverse metric. Lifting the topological sector of this action to three dimensions produces several WessZumino like terms which encode the bivector generalization of the Courant bracket. This bracket may be familiar to physicists through the (Hijk,F k ij,Qjk i,Rijk) notation for nongeometric backgrounds introduced by SheltonTaylorWecht. The nongeometricity of the string theory in encoded in the global properties of the bivector, when the bivector is a section then the string theory is geometric. Another interesting situation emerges when one considers membrane actions which are not equivalent to string theories on the boundary of the membrane. Such a situation arises when one attempts to describe the socalled Rspace (the third Tdual of a T 3 with H3 flux). This model appears to be, at least classically, described by a membrane sigma model, not a string theory. Examples of geometric backgrounds with bivector couplings and nonvanishing Qcoefficients are provided by gauged WZW models. 1
Explaining the Pure Spinor Formalism for the Superstring
 JHEP 0801 (2008) 065, arXiv:0712.0324
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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 ..."
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Cited by 21 (0 self)
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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.
NonCritical Pure Spinor Superstrings
, 2006
"... We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spi ..."
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Cited by 15 (3 self)
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We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the noncritical pure spinor space, which is different from the tendimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the noncritical pure spinor type IIA superstring on AdS4 with RR 4form flux.
Oneloop Superstring Amplitude From Integrals on
 Pure Spinors Space,” JHEP 0912 (2009) 034. [arXiv:0910.3405 [hepth
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BRST quantization of the pure spinor superstring
, 2007
"... We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and nonminimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then procee ..."
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Cited by 11 (2 self)
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We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and nonminimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then proceeding to BRST quantize this system. Our analysis includes the introduction of constant ghosts and associated auxiliary fields needed to gauge fix symmetries associated with zero modes. All fields introduced in the process of quantization can be integrated out explicitly, resulting in the prescriptions for computing scattering amplitudes that have appeared previously in the literature. The zero mode insertions in the path integral follow from the integration
Instantons beyond topological theory
 I
"... Abstract. Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the antiinstantons are absent, and the perturbative corrections are reduced to oneloop. We analyze the corresponding models as full quantum field theories, beyond th ..."
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Cited by 10 (3 self)
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Abstract. Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the antiinstantons are absent, and the perturbative corrections are reduced to oneloop. We analyze the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories. In Part I we describe the class of models under study and present our results in the case of onedimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyze explicitly. Part II will be devoted to supersymmetric twodimensional sigma models and fourdimensional YangMills