scholarly journals From symmetric product CFTs to AdS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Rajesh Gopakumar ◽  
Bob Knighton ◽  
Pronobesh Maity
Keyword(s):  
String Theory ◽  
Matrix Model ◽  
Spectral Curve ◽  
Underlying Mechanism ◽  
Covering Space ◽  
Symmetric Product ◽  
Branched Covers ◽  
World Sheet ◽  
Absolute Value ◽  
Finite Sum

Abstract Correlators in symmetric orbifold CFTs are given by a finite sum of admissible branched covers of the 2d spacetime. We consider a Gross-Mende like limit where all operators have large twist, and show that the corresponding branched covers can be described via a Penner-like matrix model. The limiting branched covers are given in terms of the spectral curve for this matrix model, which remarkably turns out to be directly related to the Strebel quadratic differential on the covering space. Interpreting the covering space as the world-sheet of the dual string theory, the spacetime CFT correlator thus has the form of an integral over the entire world-sheet moduli space weighted with a Nambu-Goto-like action. Quite strikingly, at leading order this action can also be written as the absolute value of the Schwarzian of the covering map.Given the equivalence of the symmetric product CFT to tensionless string theory on AdS3, this provides an explicit realisation of the underlying mechanism of gauge-string duality originally proposed in [1] and further refined in [2].

scholarly journals D-instantons, string field theory and two dimensional string theory

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Scattering Amplitude ◽  
Two Dimensional ◽  
World Sheet ◽  
Numerical Result ◽  
Instanton Contribution ◽  
The Matrix

Abstract In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.

scholarly journals JT gravity limit of Liouville CFT and matrix model

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Kenta Suzuki ◽  
Tadashi Takayanagi
Keyword(s):  
String Theory ◽  
Matrix Model ◽  
Semiclassical Limit ◽  
Liouville Theory ◽  
Partition Functions ◽  
Two Dimensional ◽  
De Sitter ◽  
World Sheet ◽  
Boundary Terms ◽  
The World

Abstract In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of c < 1 two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in c = 1 matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.

scholarly journals Free field world-sheet correlators for AdS3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Andrea Dei ◽  
Matthias R. Gaberdiel ◽  
Rajesh Gopakumar ◽  
Bob Knighton
Keyword(s):  
String Theory ◽  
Free Field ◽  
Delta Function ◽  
Branched Covers ◽  
World Sheet ◽  
Incidence Relation ◽  
Genus Zero ◽  
Special Cases

Abstract We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ psu 1 1 2 1 world-sheet theory to constrain the correlators of string theory on AdS3× S3× 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

scholarly journals Quantum spectral curve for (q, t)-matrix model

2017 ◽  
Vol 108 (2) ◽  
pp. 413-424 ◽  
Author(s):  
Yegor Zenkevich
Keyword(s):  
Matrix Model ◽  
Spectral Curve ◽  
T Matrix

scholarly journals QUANTUM RINGS AND RECURSION RELATIONS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (16) ◽  
pp. 1419-1425 ◽  
Author(s):  
SHAMIT KACHRU
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Ring Structure ◽  
Two Dimensional ◽  
Recursion Relations ◽  
Quantum Rings ◽  
Bulk Scattering

I study tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.

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