On W algebras commuting with a set of screenings

Litvinov, A. V.; Spodyneiko, Lev

doi:10.1007/jhep11(2016)138

Cited by 42 publications

(76 citation statements)

References 20 publications

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“…Moreover, we assume that only odd-spin integrals of motion are present: I free 2k = 0, because this is what we expect for the theory which has O(N ) symmetry in some limit. With these conditions specified one can find a series of solutions for every N ≥ 3 which depends on a continuous parameter b (see appendix A and [22] for more details). Since the cases N = 2n + 1 and N = 2n + 2 are different we consider them separately.…”

Section: Dual Lagrangiansmentioning

confidence: 99%

“…It changes the roots α s →α s as well as shifts the charges of the exponential fields according to a → a + α r . As explained in [22], the operator R r can be lifted to the operator, called fermionic reflection operator, acting on the total "off-shell" correlation functions. Therefore it serves as an isomorphism between different conformal field theories, corresponding to different root systems.…”

Section: Conformal Field Theory Reflection Operatormentioning

confidence: 99%

“…In this section, we formulate the dual sigma model description of the same theory. The duality description emerges from the following fact [22]. Consider two exponential operators e (αr,ϕ) , r = 1, 2, such that (α r , α r ) = −1 and (α 1 , α 2 ) = 0.…”

Section: Ricci Flow Equationsmentioning

confidence: 99%

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On dual description of the deformed O(N) sigma model

Litvinov

Spodyneiko

2018

J. High Energ. Phys.

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We study dual strong coupling description of integrability-preserving deformation of the O(N ) sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the η−deformed O(N ) sigma-model after T −duality transformation.(1.5)Clearly, this procedure breaks the left symmetry, but preserves the right one. It can be shown that the model is still enjoys the zero curvature representation and hence possesses the integrability property. In this paper we consider the case of O(N ) sigma-model, i.e. we take G = SO(N ) and H = SO(N − 1). Integrability of this sigma-model at the quantum level has been first demonstrated by Polyakov [10]. As QFT O(N ) sigma-model corresponds to an asymptotically free theory with a dynamically generated mass scale. It describes scattering of N mesons in the vector representation of the global O(N ) group [11,12]. The scattering matrix for these mesons is strongly constrained by integrability, which implies, in particular, the absence of particle production and factorization of the multi-particles amplitudes into the product of the two-particle scattering. These requirements plus the conditions of crossing invariance and unitarity are so strong that allow one to compute the S-matrix exactly. The two-particle S−matrix for the O(N ) sigma-model has been found by Alexander and Alexey Zamolodchikov in their seminal paper [13]. It has an explicit form S kl ij (θ) = δ ij δ kl S 1 (θ) + δ ik δ jl S 2 (θ) + δ il δ jk S 3 (θ), S 3 (θ) = S 1 (iπ − θ), S 1 (θ) = − 2iπ (N − 2)(iπ − θ) S 2 (θ), S 2 (θ) = Q(θ)Q(iπ − θ), (1.6)

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Section: Dual Lagrangiansmentioning

confidence: 99%

Section: Conformal Field Theory Reflection Operatormentioning

confidence: 99%

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On dual description of the deformed O(N) sigma model

Litvinov

Spodyneiko

2018

J. High Energ. Phys.

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“…The first principle quantization of such theories seems to be a very interesting problem. In the recent works [109,110], an important step in this direction was taken where a one parameter deformation was found of the set of "circular brane" local integrals of motion introduced in ref. [111].…”

Section: Jhep01(2018)021mentioning

confidence: 99%

Quantum transfer-matrices for the sausage model

Bazhanov

Kotousov

Lukyanov

2018

J. High Energ. Phys.

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In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -the sausage model. Our consideration is based on the so-called ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method. The approach allowed us to explore the integrable structures underlying the quantum O(3)/sausage model. Among the obtained results is a system of non-linear integral equations for the computation of the vacuum eigenvalues of the quantum transfer-matrices.

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“…The quotient of U q (gl 1 ) by the two-sided ideal generated by operators, which act as 0 on any such tensor product is a certain W algebra depending on three integer parameters k, n, m. These algebras (or, rather, their conformal limits) appear recently in [31], [22] in a different context, the formulas for screening operators for these algebras follows from the Lemmas 5.1, 5.2. We hope to study these algebras in more details elsewhere.…”

Section: Now We Want To Consider Tensor Productsmentioning

confidence: 99%

Plane partitions with a “pit”: generating functions and representation theory

Bershtein

Feigin

Merzon

2018

Sel. Math. New Ser.

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We study plane partitions satisfying condition a n+1,m+1 = 0 (this condition is called "pit") and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions.Such plane partitions label the basis vectors in certain representations of quantum toroidal gl 1 algebra, therefore our formulas can be interpreted as the characters of these representations. The resulting formulas resemble formulas for characters of tensor representations of Lie superalgebra gl m|n . We discuss representation theoretic interpretation of our formulas using q-deformed W -algebra gl m|n .1 Usually a formula is called bosonic if it equals a linear combination of characters of algebra of polynomials. In our case bosonic formula is a combination of terms q ∆ /(q) n+m ∞ .

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On W algebras commuting with a set of screenings

Abstract: Abstract:We consider the problem of classification of all W algebras which commute with a set of exponential screening operators. Assuming that the W algebra has a nontrivial current of spin 3, we find equations satisfied by the screening operators and classify their solutions.

Cited by 42 publications

References 20 publications

On dual description of the deformed O(N) sigma model

On dual description of the deformed O(N) sigma model

Quantum transfer-matrices for the sausage model

Plane partitions with a “pit”: generating functions and representation theory

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