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Gregory P. Korchemsky - One of the best experts on this subject based on the ideXlab platform.
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Scaling function in AdS/CFT from the O(6) Sigma Model
Nuclear Physics, 2009Co-Authors: Zoltan Bajnok, B. Basso, János Balog, Gregory P. Korchemsky, László PallaAbstract:Abstract Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N = 4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) Sigma Model. We calculate this function by combining the two-loop correction to the energy density for the O ( n ) Model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N = 4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.
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scaling function in ads cft from the o 6 Sigma Model
Nuclear Physics, 2009Co-Authors: Zoltan Bajnok, B. Basso, János Balog, Gregory P. Korchemsky, László PallaAbstract:Abstract Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N = 4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) Sigma Model. We calculate this function by combining the two-loop correction to the energy density for the O ( n ) Model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N = 4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.
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Embedding nonlinear O(6) Sigma Model into N=4 super-Yang–Mills theory
Nuclear Physics, 2009Co-Authors: B. Basso, Gregory P. KorchemskyAbstract:Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N=4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6) Sigma Model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O(6) Sigma Model embedded into AdS5×S5.
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embedding nonlinear o 6 Sigma Model into n 4 super yang mills theory
Nuclear Physics, 2009Co-Authors: B. Basso, Gregory P. KorchemskyAbstract:Abstract Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N = 4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O ( 6 ) Sigma Model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O ( 6 ) Sigma Model embedded into AdS 5 × S 5 .
Ruijun Wu - One of the best experts on this subject based on the ideXlab platform.
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symmetries and conservation laws of a nonlinear Sigma Model with gravitino
Journal of Geometry and Physics, 2018Co-Authors: Jurgen Jost, Enno Kesler, Jurgen Tolksdorf, Ruijun WuAbstract:Abstract We study the symmetries and invariances of a version of the action functional of the nonlinear Sigma Model with gravitino, as considered in Jost et al. (2017). The action is invariant under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms. In particular cases the functional possesses a degenerate supersymmetry. The corresponding conservation laws lead to a geometric interpretation of the energy–momentum tensor and supercurrent as holomorphic sections of appropriate bundles.
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partial regularity for a nonlinear Sigma Model with gravitino in higher dimensions
Calculus of Variations and Partial Differential Equations, 2018Co-Authors: Jurgen Jost, Ruijun WuAbstract:We study the regularity problem of the nonlinear Sigma Model with gravitino fields in higher dimensions. After setting up the geometric Model, we derive the Euler–Lagrange equations and consider the regularity of weak solutions defined in suitable Sobolev spaces. We show that any weak solution is actually smooth under some smallness assumption for certain Morrey norms. By assuming some higher integrability of the vector spinor, we can show a partial regularity result for stationary solutions, provided the gravitino is critical, which means that the corresponding supercurrent vanishes. Moreover, in dimension $$<6$$ , partial regularity holds for stationary solutions with respect to general gravitino fields.
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regularity of solutions of the nonlinear Sigma Model with gravitino
Communications in Mathematical Physics, 2018Co-Authors: Jurgen Jost, Enno Kesler, Jurgen Tolksdorf, Ruijun WuAbstract:We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear Sigma Model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler–Lagrange equations of the two-dimensional nonlinear Sigma Model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Riviere’s regularity theory and Riesz potential theory.
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partial regularity for a nonlinear Sigma Model with gravitino in higher dimensions
arXiv: Differential Geometry, 2017Co-Authors: Jurgen Jost, Ruijun WuAbstract:We study the regularity problem of the nonlinear Sigma Model with gravitino fields in higher dimensions. After setting up the geometric Model, we derive the Euler--Lagrange equations and consider the regularity of weak solutions defined in suitable Sobolev spaces. We show that any weak solution is actually smooth under some smallness assumption for certain Morrey norms. By assuming some higher integrability of the vector spinor, we can show a partial regularity result for stationary solutions, provided the gravitino is critical, which means that the corresponding supercurrent vanishes. Moreover, in dimension less than 6, partial regularity holds for stationary solutions with respect to general gravitino fields.
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coarse regularity of solutions to a nonlinear Sigma Model with l p gravitino
arXiv: Analysis of PDEs, 2017Co-Authors: Jurgen Jost, Ruijun WuAbstract:The regularity of weak solutions of a two-dimensional nonlinear Sigma Model with coarse gravitino is shown. Here the gravitino is only assumed to be in $L^p$ for some $p>4$. The precise regularity results depend on the value of $p$.
B. Basso - One of the best experts on this subject based on the ideXlab platform.
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Scaling function in AdS/CFT from the O(6) Sigma Model
Nuclear Physics, 2009Co-Authors: Zoltan Bajnok, B. Basso, János Balog, Gregory P. Korchemsky, László PallaAbstract:Abstract Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N = 4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) Sigma Model. We calculate this function by combining the two-loop correction to the energy density for the O ( n ) Model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N = 4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.
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scaling function in ads cft from the o 6 Sigma Model
Nuclear Physics, 2009Co-Authors: Zoltan Bajnok, B. Basso, János Balog, Gregory P. Korchemsky, László PallaAbstract:Abstract Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N = 4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) Sigma Model. We calculate this function by combining the two-loop correction to the energy density for the O ( n ) Model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N = 4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.
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Embedding nonlinear O(6) Sigma Model into N=4 super-Yang–Mills theory
Nuclear Physics, 2009Co-Authors: B. Basso, Gregory P. KorchemskyAbstract:Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N=4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6) Sigma Model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O(6) Sigma Model embedded into AdS5×S5.
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embedding nonlinear o 6 Sigma Model into n 4 super yang mills theory
Nuclear Physics, 2009Co-Authors: B. Basso, Gregory P. KorchemskyAbstract:Abstract Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N = 4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O ( 6 ) Sigma Model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O ( 6 ) Sigma Model embedded into AdS 5 × S 5 .
Alberto S Cattaneo - One of the best experts on this subject based on the ideXlab platform.
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On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
Communications in Mathematical Physics, 2020Co-Authors: Alberto S Cattaneo, Nima Moshayedi, Konstantin WernliAbstract:We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum Grothendieck BFV operator on the total space of states is a differential, i.e. squares to zero, which is necessary for a well-defined BV cohomology.
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the poisson Sigma Model on closed surfaces
Journal of High Energy Physics, 2012Co-Authors: Francesco Bonechi, Alberto S Cattaneo, Pavel MnevAbstract:Using methods of formal geometry, the Poisson Sigma Model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kahler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other Sigma Models, at least of the AKSZ type.
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coisotropic submanifolds in poisson geometry and branes in the poisson Sigma Model
Letters in Mathematical Physics, 2004Co-Authors: Alberto S Cattaneo, Giovanni FelderAbstract:General boundary conditions (‘branes’) for the Poisson Sigma Model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.
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on the globalization of kontsevich s star product and the perturbative poisson Sigma Model
Progress of Theoretical Physics Supplement, 2001Co-Authors: Alberto S Cattaneo, Giovanni FelderAbstract:The globalization of Kontsevich's local formula (resp., the perturbative expansion of the Poisson Sigma Model) is described in down-to-earth terms.
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on the aksz formulation of the poisson Sigma Model
arXiv: Quantum Algebra, 2001Co-Authors: Alberto S Cattaneo, Giovanni FelderAbstract:We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of Sigma Models on manifolds with boundary. We show that a special case of this construction yields the Batalin-Vilkovisky action functional of the Poisson Sigma Model on a disk. As we have shown in a previous paper, the perturbative quantization of this Model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.
Arkady A Tseytlin - One of the best experts on this subject based on the ideXlab platform.
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kappa symmetry of superstring Sigma Model and generalized 10d supergravity equations
Journal of High Energy Physics, 2016Co-Authors: Arkady A Tseytlin, Linus WulffAbstract:We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X a and imply the one-loop scale invariance of the GS Sigma Model. In the special case when X a is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring Sigma Model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv:1511.05795 . These equations depend on two vectors X a and K a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X a = X a + K a ). In the special case of K a = 0 one finds that X a = ∂ a ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K a is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS n × S n Sigma Models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS Sigma Model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.
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pohlmeyer reduction of ads5 s5 superstring Sigma Model
Nuclear Physics, 2008Co-Authors: Maxim Grigoriev, Arkady A TseytlinAbstract:Abstract Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS 5 × S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” version of the corresponding Sigma Model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string Sigma Model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-Abelian Toda type: a gauged WZW Model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW Model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced Model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS 2 × S 2 superstring Model the reduced theory is indeed supersymmetric: it is equivalent to the N = 2 supersymmetric extension of the sine-Gordon Model.
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Sigma Model approach to string theory effective actions with tachyons
Journal of Mathematical Physics, 2001Co-Authors: Arkady A TseytlinAbstract:Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the Sigma Model approach. In particular, we demonstrate that the renormalized partition function Z(T,A) of the boundary Sigma Model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F2(dF)2 derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure −T2e−T, but it vanishes in the NSR string case.
