scholarly journals α′-corrections and their double formulation

2021 ◽  
Author(s):  
Eric Lescano
Keyword(s):  
Field Theory ◽  
Graduate Students ◽  
String Theory ◽  
Closed String ◽  
Basic Knowledge ◽  
Santiago De Compostela ◽  
Double Field Theory

Abstract The present notes are based on three lectures, each ninety minutes long, prepared for the school “Integrability, Dualities and Deformations”, that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually. These lectures, aimed at graduate students, require only a basic knowledge of string theory. The main goal is to introduce α′-corrections to the gravitational sector of different formulations of closed string theory and to reformulate them using novel techniques based on double field theory.

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 String theory at order α′2 and the generalized Bergshoeff-de Roo identification

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stanislav Hronek ◽  
Linus Wulff
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Strong Evidence ◽  
Degrees Of Freedom ◽  
Heterotic String ◽  
Lorentz Transformations ◽  
Covariant Formalism ◽  
Double Field Theory ◽  
Two Parameter ◽  
Parameter Deformation

Abstract It has been shown by Marques and Nunez that the first α′-correction to the bosonic and heterotic string can be captured in the O(D, D) covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of α′-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct α′2-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.

scholarly journals Dynamics of perturbations in Double Field Theory & non-relativistic string theory

2015 ◽  
Vol 2015 (12) ◽  
pp. 1-33 ◽  
Author(s):  
Sung Moon Ko ◽  
Charles M. Melby-Thompson ◽  
René Meyer ◽  
Jeong-Hyuck Park
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Relativistic String ◽  
Double Field Theory

scholarly journals The OD, D geometry of string theory

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
David S. Berman ◽  
Chris D. A. Blair ◽  
Emanuel Malek ◽  
Malcolm J. Perry
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Covariant Derivative ◽  
Double Field Theory ◽  
Metric Connection

We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the OD, D structure. The connection is simultaneously torsionful and flat. Using this connection, one may construct a proper covariant derivative for double field theory. We then write the doubled action in terms of the generalised torsion of this connection. This action then exactly reproduces that required for double field theory and gauged supergravity.

scholarly journals Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

2018 ◽  
Vol 168 ◽  
pp. 07004 ◽  
Author(s):  
Taejin Lee
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
String Theory ◽  
String Field Theory ◽  
Fock Space ◽  
Proper Time ◽  
Path Integrals ◽  
Open String ◽  
Closed String ◽  
Quantized String

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

scholarly journals Non-Riemannian isometries from double field theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Chris D. A. Blair ◽  
Gerben Oling ◽  
Jeong-Hyuck Park
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Relativistic String ◽  
Noether Symmetries ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Killing Spinors ◽  
Double Field Theory ◽  
Riemannian Geometries ◽  
Killing Equations

Abstract We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgrounds and show that they admit an infinite-dimensional algebra of isometries which includes a particular type of supertranslations. These symmetries correspond to known worldsheet Noether symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret as isometries of its non-Riemannian doubled background. We further consider the extension to supersymmetric double field theory and show that the corresponding Killing spinors can depend arbitrarily on the non-Riemannian directions, leading to “supersupersymmetries” that square to supertranslations.

scholarly journals THE STOYANOVSKY–RIBAULT–TESCHNER MAP AND STRING SCATTERING AMPLITUDES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4003-4034 ◽  
Author(s):  
GASTON GIRIBET ◽  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
String Theory ◽  
Correlation Functions ◽  
Central Charge ◽  
Closed String ◽  
Liouville Theory ◽  
Type Reduction ◽  
Point Correlation ◽  
Liouville Field Theory

Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL (2,ℂ)k/ SU (2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFT's as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k → 0 and show that, at the point k = 0, the Stoyanovsky–Ribault–Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes cL = -2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory.

scholarly journals More stringy effects in target space from Double Field Theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Chen-Te Ma ◽  
Franco Pezzella
Keyword(s):  
Field Theory ◽  
Space Dimension ◽  
Mass Term ◽  
Closed String ◽  
Target Space ◽  
Gauge Transformations ◽  
Double Field Theory ◽  
Quadratic Action ◽  
Lower Dimensional ◽  
Compactified Space

Abstract In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR− 2. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with (NL = 1, NR = 1) such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states (NL = 2, NR = 0) and (NL = 0, NR = 2) which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states (NL = 1, NR = 1). A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.

scholarly journals Cutkosky rules and unitarity (violation) in D-instanton amplitudes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Effective Action ◽  
Open String ◽  
Closed String ◽  
World Sheet ◽  
Superstring Theory ◽  
Reality Condition ◽  
Instanton Contribution ◽  
Integration Cycle

Abstract In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real. The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories.

scholarly journals TACHYON DYNAMICS IN OPEN STRING THEORY

2005 ◽  
Vol 20 (24) ◽  
pp. 5513-5656 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
String Field Theory ◽  
Quantum Dynamics ◽  
Open String ◽  
Closed String ◽  
Two Dimensional ◽  
Potential Models ◽  
Conformal Field ◽  
String Background

In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane–antibrane system in string theory. The various string theoretic methods used for this study include techniques of two-dimensional conformal field theory, open string field theory, boundary string field theory, noncommutative solitons, etc. We also describe various attempts to understand these results using field theoretic methods. These field theory models include toy models like singular potential models and p-adic string theory, as well as more realistic version of the tachyon effective action based on Dirac–Born–Infeld type action. Finally we study closed string background produced by the "decaying" unstable D-branes, both in the critical string theory and in the two-dimensional string theory, and describe the open string completeness conjecture that emerges out of this study. According to this conjecture the quantum dynamics of an unstable D-brane system is described by an internally consistent quantum open string field theory without any need to couple the system to closed strings. Each such system can be regarded as a part of the "hologram" describing the full string theory.

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