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.

CORRELATION FUNCTIONS AND ZERO MODES ON HIGHER GENUS RIEMANN SURFACES

1988 ◽  
Vol 03 (04) ◽  
pp. 841-860 ◽  
Author(s):  
M. BONINI ◽  
R. IENGO
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Covariant Formulation ◽  
Two Dimensional ◽  
Zero Modes ◽  
Modular Transformation ◽  
Higher Genus

We describe systematically the propagators and the zero modes of the various two dimensional fields which appear in the construction of the scattering amplitudes in the string theory, within the framework of the covariant formulation, and we discuss also their modular transformation properties.

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 LANGLANDS DUALITY IN LIOUVILLE-$H^3_+$ WZNW CORRESPONDENCE

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3137-3170 ◽  
Author(s):  
GASTON GIRIBET ◽  
YU NAKAYAMA ◽  
LORENA NICOLÁS
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Liouville Theory ◽  
Hamiltonian Reduction ◽  
Langlands Correspondence ◽  
Conformal Field ◽  
Langlands Duality ◽  
Dual Version ◽  
Free Field Realization ◽  
Wznw Model

We show a physical realization of the Langlands duality in correlation functions of [Formula: see text] WZNW model. We derive a dual version of the Stoyanovky–Riabult–Teschner (SRT) formula that relates the correlation function of the [Formula: see text] WZNW and the dual Liouville theory to investigate the level duality k - 2 → (k - 2)-1 in the WZNW correlation functions. Then, we show that such a dual version of the [Formula: see text]-Liouville relation can be interpreted as a particular case of a biparametric family of nonrational conformal field theories (CFT's) based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new nonrational CFT's and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the Drinfeld–Sokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the [Formula: see text] WZNW model. Our new identity for the correlation functions of [Formula: see text] WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically.

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.

MODULAR INVARIANT ONE-POINT CORRELATION FUNCTIONS FOR SU(2) WESS-ZUMINO MODEL

1992 ◽  
Vol 07 (25) ◽  
pp. 6257-6272 ◽  
Author(s):  
O.D. ANDREEV
Keyword(s):  
Correlation Functions ◽  
Riemann Surfaces ◽  
Free Field ◽  
Necessary Condition ◽  
Modular Invariant ◽  
Field Representation ◽  
Conformal Field ◽  
Higher Genus ◽  
Point Correlation ◽  
Zumino Model

We calculate one-point correlation functions of SU(2) Wess-Zumino model (WZM) on a torus using the Wakimoto free field representation. Their modular invariance is proved. It is a necessary condition of extending the WZ conformal field theory to higher genus Riemann surfaces.

scholarly journals CORRELATION FUNCTIONS AND MULTICRITICAL FLOWS IN c<1 STRING THEORY

1995 ◽  
Vol 10 (04) ◽  
pp. 477-498 ◽  
Author(s):  
SURESH GOVINDARAJAN ◽  
T. JAYARAMAN ◽  
VARGHESE JOHN
Keyword(s):  
String Theory ◽  
Matrix Models ◽  
Correlation Functions ◽  
Ring Structure ◽  
Tree Level ◽  
Vertex Operators ◽  
Minimal Models

We compute all string tree level correlation functions of vertex operators in c < 1 string theory. This is done by using the ring structure of the theory. In order to study the multicritical behavior, we calculate the correlation functions after perturbation by physical vertex operators. We show that the (2k − 1, 2) models can be obtained from the (1, 2) model and the minimal models can be obtained from the (1, p) model by perturbing the action with appropriate physical operators. Our results are consistent with known results from matrix models.

scholarly journals D-branes in AdS3 × S3 × 𝕋4 at k = 1 and their holographic duals

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Bob Knighton ◽  
Jakub Vošmera
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Moduli Space ◽  
Free Field ◽  
Boundary States ◽  
Holographic Duals ◽  
Direct Correspondence

Abstract String theory on AdS3× S3× 𝕋4 with minimal k = 1 NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT Sym(𝕋4), thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk.

scholarly journals String theory on AdS3 × M7 in the tensionless limit

2020 ◽  
Vol 29 (06) ◽  
pp. 2030005
Author(s):  
Gaston Giribet
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Correlation Functions ◽  
Target Space ◽  
Special Point ◽  
String Length ◽  
Special Limit

We review old and recent results on a special limit of string theory on [Formula: see text] with pure NS–NS fluxes: the limit in which the string length [Formula: see text] equals the [Formula: see text] radius [Formula: see text]. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the noncompactness of the boundary CFT target space, and on how these features change when the point [Formula: see text] is approached. Also, we briefly review the recent proposals for exact realizations of AdS/CFT correspondence at this special point.

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

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