scholarly journals BEYOND THE LARGE N LIMIT: NON-LINEAR W∞ AS SYMMETRY OF THE SL(2,R)/U(1) COSET MODEL

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 55-81 ◽  
Author(s):  
IOANNIS BAKAS ◽  
ELIAS KIRITSIS
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Free Field ◽  
Symmetry Algebra ◽  
Linear Deformation ◽  
Coset Model ◽  
Large N ◽  
Free Field Realization ◽  
Non Linear ◽  
Background Charge

We show that the symmetry algebra of the SL(2,R)k/ U(1) coset model is a non-linear deformation of W∞, characterized by k. This is a universal W-algebra which linearizes in the large k limit and truncates to WN for K=-N. Using the theory of non-compact parafermions we construct a free field realization of the non-linear W∞ in terms of two bosons with background charge. The W-characters of all unitary SL(2,R)/ U(1) representations are computed. Applications to the physics of 2-d black hole backgrounds are also discussed and connections with the KP approach to c=1 string theory are outlined.

scholarly journals BOSONIZATION OF A TOPOLOGICAL COSET MODEL AND NON-CRITICAL STRING THEORY

1994 ◽  
Vol 09 (06) ◽  
pp. 541-547 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
String Theory ◽  
Free Field ◽  
Superconformal Algebra ◽  
Minimal Models ◽  
Total Derivative ◽  
Coset Model ◽  
Free Field Realization ◽  
Topological Field ◽  
The Subject ◽  
Coset Models

We analyze the relation between a topological coset model based on super SL(2, R)/U(1) coset and non-critical string theory by using free field realization. We show that the twisted N=2 algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST non-trivial state of ghost number 0 (generator of the ground ring for c=1 gravity). The relation between non-critical strings and topological field theories is the subject of current interest. It has long been suggested that the latter theories describe the unbroken phase of gravity,1 but their precise relation has not been clear. It has been known that the twisting of N=2 superconformal field theory gives rise to topological theory.1,2 This suggests that any non-critical string theories may have hidden N=2 superconformal symmetry. Indeed, several authors have observed that the BRST current and the antighost field b(z) generate an algebra that is quite similar but apparently not identical to the N=2 superconformal algebra.3 It turns out that the BRST current can be modified by total derivative terms so that the antighost and the physical BRST current exactly generate a topologically twisted N=2 superconformal algebra.4,5 This does not identify, however, the structure of the models with N=2 symmetry. Recently, rather non-trivial correspondence between super SL(2, R)k/U(1) coset model6 and c=1 string has been analyzed through twisted N=2 structure. Mukhi and Vafa7 have revealed an amazing correspondence between these two models for k=3. In this letter, we discuss the relation of these models and the generalization of the correspondence to the minimal models coupled to gravity by means of the free field realization. We find that there is another interesting correspondence for k=1. Super SL(2, R)k/U(1) model is described by the bosonic coset model of SL(2, R)k×U(1)/U(1).8 For a representation of SL(2, R)k, we use the following

scholarly journals LIE SUPERALGEBRA AND EXTENDED TOPOLOGICAL CONFORMAL SYMMETRY IN NON-CRITICAL W3-STRINGS

1994 ◽  
Vol 09 (33) ◽  
pp. 3063-3075 ◽  
Author(s):  
KATSUSHI ITO ◽  
HIROAKI KANNO
Keyword(s):  
String Theory ◽  
Root System ◽  
Simple Root ◽  
Similarity Transformation ◽  
Conformal Symmetry ◽  
Free Field ◽  
Lie Superalgebra ◽  
Hamiltonian Reduction ◽  
Free Field Realization ◽  
Quantum Hamiltonian

We obtain a new free field realization of N = 2 super W3-algebra using the technique of quantum Hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra sl (3|2)(1) associated with a non-standard sl (2) embedding. After twisting and a similarity transformation, this W-algebra can be identified as the extended topological conformal algebra of non-critical W3 string theory.

scholarly journals The 𝒩 = 4 coset model and the higher spin algebra

2020 ◽  
Vol 35 (11n12) ◽  
pp. 2050046
Author(s):  
Changhyun Ahn ◽  
Dong-gyu Kim ◽  
Man Hea Kim
Keyword(s):  
Free Field ◽  
Operator Product ◽  
Coupling Constant ◽  
Coset Model ◽  
Matrix Generalization ◽  
Free Field Realization ◽  
Coset Construction ◽  
The Matrix ◽  
Higher Spin ◽  
Structure Constants

By computing the operator product expansions between the first two [Formula: see text] higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large [Formula: see text] ’t Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins [Formula: see text] and [Formula: see text] with manifest [Formula: see text] symmetry at vanishing ’t Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the [Formula: see text] [Formula: see text] algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two [Formula: see text] invariant tensors. We also describe the [Formula: see text] higher spin generators, by using the above coset construction results, for general superspin [Formula: see text] in terms of oscillators in the matrix generalization of [Formula: see text] Vasiliev higher spin theory at nonzero ’t Hooft-like coupling constant. We obtain the [Formula: see text] higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins [Formula: see text] and [Formula: see text].

scholarly journals On deformations and extensions of Diff(S2)

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Martín Enríquez Rojo ◽  
Tomáš Procházka ◽  
Ivo Sachs
Keyword(s):  
Vector Fields ◽  
Free Field ◽  
Symmetry Algebra ◽  
Null Infinity ◽  
Central Extensions ◽  
Asymptotically Flat ◽  
Free Field Realization ◽  
The One ◽  
Area Preserving ◽  
Parameter Deformation

Abstract We investigate the algebra of vector fields on the sphere. First, we find that linear deformations of this algebra are obstructed under reasonable conditions. In particular, we show that hs[λ], the one-parameter deformation of the algebra of area-preserving vector fields, does not extend to the entire algebra. Next, we study some non-central extensions through the embedding of $$ \mathfrak{vect} $$ vect (S2) into $$ \mathfrak{vect} $$ vect (ℂ*). For the latter, we discuss a three parameter family of non-central extensions which contains the symmetry algebra of asymptotically flat and asymptotically Friedmann spacetimes at future null infinity, admitting a simple free field realization.

scholarly journals Higher genus correlators for tensionless AdS3 strings

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bob Knighton
Keyword(s):  
Perturbation Theory ◽  
String Theory ◽  
Moduli Space ◽  
Strong Evidence ◽  
Correlation Functions ◽  
Free Field ◽  
Tree Level ◽  
Branched Covering ◽  
Free Field Realization ◽  
Higher Genus

Abstract It was recently shown in [1] that tree-level correlation functions in tensionless string theory on AdS3 × S3 × $$ {\mathbbm{T}}^4 $$ T 4 match the expected form of correlation functions in the symmetric orbifold CFT on $$ {\mathbbm{T}}^4 $$ T 4 in the large N limit. This analysis utilized the free-field realization of the $$ \mathfrak{psu}{\left(1,\left.1\right|2\right)}_1 $$ psu 1 1 2 1 Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of AdS3. In particular, this identity implied the unusual feature that the string theory correlators localize to points in the moduli space for which the worldsheet covers the boundary of AdS3 with specified branching near the insertion points. In this work we generalize this analysis past the tree-level approximation, demonstrating its validity to higher genus worldsheets, and in turn providing strong evidence for this incarnation of the AdS/CFT correspondence at all orders in perturbation theory.

scholarly journals SO(3)×U(1) Isometric Instantons with Non-Abelian Hair in Four-Dimensional String Theory

1997 ◽  
Vol 12 (25) ◽  
pp. 1847-1858
Author(s):  
Adrián R. Lugo
Keyword(s):  
String Theory ◽  
Type Ii ◽  
Dimensional Solution ◽  
Coset Model

We compute the exact effective string vacuum backgrounds of the level k=81/19 SU(2,1)/U(1) coset model. A compact SU(2) isometry present in this seven-dimensional solution allows one to interpret it after compactification as a four-dimensional non-Abelian SU(2) charged instanton with a singular submanifold and an SO(3) × U(1) isometry. The semiclassical backgrounds, solutions of the type II strings, present similar characteristics

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