Chiral de Rham Complex

Malikov, Fyodor; Schechtman, Vadim; Vaintrob, Arkady

doi:10.1007/s002200050653

Cited by 226 publications

(583 citation statements)

References 11 publications

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“…Explicit computation shows that it is a homomorphism of Lie algebras (this is an example of "supersymmetric cancellation of anomalies") [FF2,MSV]. We obtain a W N -action on Ω • N , which can be exponentiated to an action of the Harish-Chandra pair (W N , Aut O N ).…”

Section: -33mentioning

confidence: 95%

Vertex Algebras and Algebraic Curves

Frenkel

Ben‐Zvi

2004

Mathematical Surveys and Monographs

499

881

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Section: -33mentioning

confidence: 95%

Vertex Algebras and Algebraic Curves

Frenkel

Ben‐Zvi

2004

Mathematical Surveys and Monographs

499

881

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“…Thus, we find the isomorphisms A 0,0 ∼ = A 1,1 and A 0,1 ∼ = A 1,2 . In fact, it can be shown [2] that the isomorphism A 0,h ∼ = A 1,h+1 persists in higher dimensions h ≥ 2 as well.…”

Section: The Perturbative Chiral Algebramentioning

confidence: 96%

“…This conformal field theory is called the free βγ system. In the mathematical literature, the sheaf Z 0,h of local operators of free βγ systems with this OPE structure is called the sheaf of chiral differential operators (CDOs) [2].…”

Section: Gluing Free Theories: Sheaf Of Chiral Differential Operatorsmentioning

confidence: 99%

“…On the other hand, its action on β is determined by imposing the condition that the OPEs among the fields β ′ and γ ′ be the same as those among β and γ. Hence, we have [2] …”

Section: The Perturbative Chiral Algebramentioning

confidence: 99%

“…The theory of CDOs had first been introduced and developed in a series of seminal papers by Malikov et al [2,3]. It has since found interesting applications in geometry and representation theory, such as mirror symmetry [4] and the study of elliptic genera [5,6,7], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

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Chiral Algebras of (0, 2) Models: Beyond Perturbation Theory

Tan

Yagi

2008

Lett Math Phys

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We explore the nonperturbative aspects of the chiral algebras of N = (0, 2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nontrivial consequences for the chiral algebra. As an example, we study the case where the target space is CP 1 , and show that worldsheet instantons trivialize the chiral algebra entirely. Consequently, supersymmetry is spontaneously broken in this model. We then turn to a closer look at the supersymmetry breaking from the viewpoint of Morse theory on loop space. We find that instantons interpolate between pairs of perturbative supersymmetric states with different fermionic numbers, hence lifting them out of the supersymmetric spectrum. Our results reveal that a "quantum" deformation of the geometry of the target space leads to a trivialization of the kernels of certain twisted Dirac operators on CP 1 .

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Geometric transitions on non‐Kähler manifolds

Knauf

2006

Fortschritte der Physik

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This article is based on the publications [1,2,3] and the author's PhD-thesis. We study geometric transitions on the supergravity level using the basic idea of [1], where a pair of nonKähler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in [3]. The non-Kähler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kähler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kähler backgrounds in type I and heterotic theory as proposed in [2]. They are found by a series of T-and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background.

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Chiral de Rham Complex

Cited by 226 publications

References 11 publications

Vertex Algebras and Algebraic Curves

Vertex Algebras and Algebraic Curves

Chiral Algebras of (0, 2) Models: Beyond Perturbation Theory

Geometric transitions on non‐Kähler manifolds

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