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15
Integrability of Type II Superstrings on RamondRamond Backgrounds in Various Dimensions
, 2007
"... Abstract: We consider type II superstrings on AdS backgrounds with RamondRamond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: noncritical superstrings on AdS2d and critical superstrings on AdSp × S p × CY. We work both in the Gr ..."
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Abstract: We consider type II superstrings on AdS backgrounds with RamondRamond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: noncritical superstrings on AdS2d and critical superstrings on AdSp × S p × CY. We work both in the Green–Schwarz and in the pure spinor formalisms. We construct a oneparameter family of flat currents (a Lax connection), leading to an infinite number of conserved nonlocal charges, which imply the classical integrability of both sigmamodels. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigmamodel. We discuss how classical κsymmetry implies oneloop conformal invariance. We consider the addition of spacefilling Dbranes to the pure spinor formalism.
ImperialTPAT20074 Pohlmeyer
, 711
"... Motivated by a desire to find a useful 2d Lorentzinvariant reformulation of the AdS5 ×S 5 superstring worldsheet theory in terms of physical degrees of freedom we investigate a Pohlmeyerreduced version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Star ..."
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Motivated by a desire to find a useful 2d Lorentzinvariant reformulation of the AdS5 ×S 5 superstring worldsheet theory in terms of physical degrees of freedom we investigate a Pohlmeyerreduced 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 kappasymmetry and introduce a new set of variables (related locally to currents but nonlocally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gaugefixed equations can be obtained from a Lagrangian of a nonabelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. The final form of the Pohlmeyerreduced theory (involving equal number of bosonic and fermionic dynamical worldsheet degrees of freedom) can be found by integrating out the 2d gauge field of the gauged WZW model. We conjecture that the reduced model has a worldsheet supersymmetry and is ultravioletfinite. We show that in the special case of the AdS2 ×S 2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the (2,2) supersymmetric extension of the sineGordon model.
DISTA2008 hepth/yymmnnn Pure Spinors for General Backgrounds †
, 803
"... We show the equivalence of the different types of pure spinor constraints geometrically derived from the Free Differential Algebras of N = 2 d=10 supergravities. Firstly, we compute the general solutions of these constraints, using both a G2 and an SO(8) covariant decomposition of the 10d chiral spi ..."
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We show the equivalence of the different types of pure spinor constraints geometrically derived from the Free Differential Algebras of N = 2 d=10 supergravities. Firstly, we compute the general solutions of these constraints, using both a G2 and an SO(8) covariant decomposition of the 10d chiral spinors. Secondly, we verify that the number of independent degrees of freedom is equal to that implied by the Poincaré pure spinor constraints sofar used for superstrings, namely twenty two. Thirdly, we show the equivalence between the FDA type IIA/B constraints among
Compactification of the Heterotic Pure Spinor
, 907
"... In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a CalabiYau background. We explicitly construct a BRST operator imposing N = 1 fourdimensional supersymmetry and sh ..."
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In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a CalabiYau background. We explicitly construct a BRST operator imposing N = 1 fourdimensional supersymmetry and show that nilpotence implies Kähler and Ricciflatness conditions. The massless spectrum is computed using this BRST operator and it agrees with the expected result. 1
2.2 Tendimensional, N = 1 Supersymmetry.................... 5
, 907
"... In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a CalabiYau background. We explicitly construct a BRST operator imposing N = 1 fourdimensional supersymmetry and sh ..."
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In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a CalabiYau background. We explicitly construct a BRST operator imposing N = 1 fourdimensional supersymmetry and show that nilpotence implies Kähler and Ricciflatness conditions. The massless spectrum is computed using this BRST operator and it agrees with the expected result.
Exploring Pure Spinor String Theory on AdS4 × CP 3
, 808
"... In this paper we formulate the pure spinor superstring theory on AdS4 × CP 3. By recasting the pure spinor action as a topological Amodel on the fermionic supercoset Osp(64)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σmodel. We then give a gauged linear σmodel which red ..."
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In this paper we formulate the pure spinor superstring theory on AdS4 × CP 3. By recasting the pure spinor action as a topological Amodel on the fermionic supercoset Osp(64)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σmodel. We then give a gauged linear σmodel which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible Dbrane boundary conditions and the principal chiral model for the fermionic supercoset. Contents
Exploring Pure Spinor String Theory on AdS4 × CP 3
, 808
"... In this paper we formulate the pure spinor superstring theory on AdS4 × CP 3. By recasting the pure spinor action as a topological Amodel on the fermionic supercoset Osp(64)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σmodel. We then give a gauged linear σmodel which red ..."
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In this paper we formulate the pure spinor superstring theory on AdS4 × CP 3. By recasting the pure spinor action as a topological Amodel on the fermionic supercoset Osp(64)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σmodel. We then give a gauged linear σmodel which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible Dbrane boundary conditions and the principal chiral model for the fermionic supercoset. Contents
of AdS5 × S 5 superstring sigma model
"... Motivated by a desire to find a useful 2d Lorentzinvariant reformulation of the AdS5 ×S 5 superstring worldsheet theory in terms of physical degrees of freedom we construct the “Pohlmeyerreduced” version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. St ..."
Abstract
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Motivated by a desire to find a useful 2d Lorentzinvariant reformulation of the AdS5 ×S 5 superstring worldsheet theory in terms of physical degrees of freedom we construct the “Pohlmeyerreduced” 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 kappasymmetry and introduce a new set of variables (related locally to currents but nonlocally 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 nonabelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gaugefixed form of the Pohlmeyerreduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The smallfluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has worldsheet supersymmetry and is ultravioletfinite. We show that in the special case of the AdS2 × S 2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sineGordon model.
Superstrings in AdS
, 2013
"... This is a comprehensive review of the worldsheet techniques for the quantization of type IIB superstring theory on the AdS5 × S5 background, using the pure spinor formalism. Particular emphasis is devoted to AdS/CFT applications, with several examples worked out in details. The review is selfcontai ..."
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This is a comprehensive review of the worldsheet techniques for the quantization of type IIB superstring theory on the AdS5 × S5 background, using the pure spinor formalism. Particular emphasis is devoted to AdS/CFT applications, with several examples worked out in details. The review is selfcontained and pedagogical. Table of contents: 1) Introduction; 2) Generalities; 3) Supercoset sigma models; 4) Quantum effective action and conformal invariance; 5) String