scholarly journals LOOP VARIABLES AND GAUGE INVARIANT EXACT RENORMALIZATION GROUP EQUATIONS FOR CLOSED STRING THEORY

2013 ◽  
Vol 28 (24) ◽  
pp. 1350116 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Open String ◽  
Background Field ◽  
Closed String ◽  
Gauge Transformations ◽  
Open Strings ◽  
Field Formalism ◽  
Exact Renormalization Group

We formulate the Exact Renormalization Group on the string worldsheet for closed string backgrounds. The same techniques that were used for open strings are used here. There are some subtleties. One is that holomorphic factorization of the closed string vertex operators does not hold in the presence of a cutoff on the Euclidean worldsheet. This introduces extra terms in the Lagrangian at the cutoff scale and they turn out to be crucial for implementing gauge invariance. This naive generalization from open string to closed string requires a massive graviton and the gauge symmetry is Abelian, just as in open string theory. Interestingly, it turns out that if one introduces a nondynamical background metric (as in background field formalism) and combines a gauge transformation on the field with a transformation on the coordinates and background metric, the graviton can be massless. Some examples of background coordinate covariant equations are worked out explicitly. A preliminary discussion of massive modes, massive gauge transformations and the role of worldsheet regulator terms is given. Some of the gauge transformations can be given a geometric meaning if space–time is assumed to be complex at some level.

scholarly journals HOLOMORPHIC FACTORIZATION AND RENORMALIZATION GROUP IN CLOSED STRING THEORY

2005 ◽  
Vol 20 (15) ◽  
pp. 1161-1176 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Open String ◽  
Renormalization Group Equation ◽  
Closed String ◽  
Group Equation ◽  
Sums Of Products

The prescription of Kawai, Lewellen and Tye for writing closed string tree amplitudes as sums of products of open string tree amplitudes, is applied to the worldsheet renormalization group equation. The main point is that regularization of the Minkowski (rather than Euclidean) worldsheet theory allows factorization into left-moving and right-moving sectors to be maintained. Explicit calculations are done for the tachyon and the (gauge fixed) graviton.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

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 OPEN-CLOSED DUALITY: LESSONS FROM MATRIX MODEL

2004 ◽  
Vol 19 (11) ◽  
pp. 841-853 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Classical Result ◽  
Open String ◽  
Closed String ◽  
Tree Level ◽  
Two Dimensional

Recent investigations involving the decay of unstable D-branes in string theory suggest that the tree level open string theory which describes the dynamics of the D-brane already knows about the closed string states produced in the decay of the brane. We propose a specific conjecture involving quantum open string field theory to explain this classical result, and show that the recent results in two-dimensional string theory are in exact accordance with this conjecture.

scholarly journals WILSON LOOPS IN OPEN STRING THEORY

1988 ◽  
Vol 03 (03) ◽  
pp. 283-287 ◽  
Author(s):  
KIYOSHI SHIRAISHI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Symmetry Breaking ◽  
Path Integral ◽  
Wilson Loop ◽  
Mass Spectra ◽  
Open String ◽  
Wilson Loops ◽  
Open Strings ◽  
Correct Weight

Wilson loop elements on torus are introduced into the partition function of open strings as Polyakov’s path integral at one-loop level. Mass spectra from compactification and expected symmetry breaking are illustrated by choosing the correct weight for the contributions from annulus and Möbius strip. We show that Jacobi’s imaginary transformation connects the mass spectra with the Wilson loops. The application to thermopartition function and cosmological implications are briefly discussed.

scholarly journals Genus zero Gopakumar-Vafa invariants from open strings

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Andrés Collinucci ◽  
Andrea Sangiovanni ◽  
Roberto Valandro
Keyword(s):  
String Theory ◽  
Open String ◽  
Genus Zero ◽  
Zero Modes ◽  
Open Strings ◽  
Crepant Resolutions ◽  
M Theory

Abstract We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid’s Pagodas, and Laufer’s examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants.

scholarly journals Classical algebraic structures in string theory effective actions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Harold Erbin ◽  
Carlo Maccaferri ◽  
Martin Schnabl ◽  
Jakub Vošmera
Keyword(s):  
String Theory ◽  
Degrees Of Freedom ◽  
Microscopic Theory ◽  
Open String ◽  
Closed String ◽  
Effective Theory ◽  
Generic Properties ◽  
Vertical Decomposition ◽  
String Background ◽  
New Framework

Abstract We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of A∞ or L∞ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten’s open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian A∞-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-brane deformations induced by changes in the closed string background.

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