scholarly journals Torus bundles, automorphisms and T-duality

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
H. Mahmood ◽  
R. A. Reid-Edwards
Keyword(s):  
Gauge Symmetry ◽  
String Theory ◽  
Moduli Space ◽  
Algebraic Structure ◽  
Operator Algebra ◽  
Target Space ◽  
Torus Bundles ◽  
Modern Context ◽  
Special Points ◽  
The Way

Abstract We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target space gauge symmetry may be enhanced. Away from such points the symmetry is broken and T-duality may be understood as a residual discrete gauge symmetry that survives this breaking. Drawing on work on connections over the space of string backgrounds, we discuss how to generalise this framework for T-duality to geometric and non-geometric backgrounds that are not full solutions of string theory, but may play an important role in exact backgrounds. Along the way we find an interesting algebraic structure and discuss its relationship with doubled geometry. We comment on non-isometric T-duality in this context.

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.

DUALITY IN STRING THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360003
Author(s):  
YOLANDA LOZANO
Keyword(s):  
String Theory ◽  
Recent Work ◽  
Moduli Space ◽  
Target Space ◽  
Duality Symmetry ◽  
Abelian Case ◽  
Superstring Theories ◽  
M Theory

Duality symmetries have played a key role in the discovery that the five consistent superstring theories in 10 dimensions emerge as different corners of the moduli space of a single unifying theory, known as M-theory. Focusing on the target space, or T, duality symmetry, we show how it can be formulated in spacetimes with abelian and non-abelian isometries. Finally, we discuss some recent work that realizes non-abelian T-duality as a consistent truncation to seven-dimensional supergravity, thus generalizing to the non-abelian case the realization of abelian T-duality at the supergravity level.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals DUALITY AND SELF-DUAL TRIPLET SOLUTIONS IN EUCLIDEAN GRAVITY

1996 ◽  
Vol 11 (34) ◽  
pp. 2669-2679
Author(s):  
SWAPNA MAHAPATRA
Keyword(s):  
String Theory ◽  
The Self ◽  
Target Space ◽  
De Sitter ◽  
Gravitational Instanton ◽  
Duality Symmetry ◽  
Sitter Solution

Starting from the self-dual “triplet” of gravitational instanton solutions in Euclidean gravity, we obtain the corresponding instanton solutions in string theory by making use of the target space duality symmetry. We show that these dual triplet solutions can be obtained from the general dual Taub-NUT de Sitter solution through some limiting procedure as in the Euclidean gravity case. The dual gravitational instanton solutions obtained here are self-dual for some cases, with respect to certain isometries, but not always.

scholarly journals Target space duality in string theory

1994 ◽  
Vol 244 (2-3) ◽  
pp. 77-202 ◽  
Author(s):  
Amit Giveon ◽  
Massimo Porrati ◽  
Eliezer Rabinovici
Keyword(s):  
String Theory ◽  
Target Space

scholarly journals Principal subspaces of twisted modules for certain lattice vertex operator algebras

2019 ◽  
Vol 30 (10) ◽  
pp. 1950048 ◽  
Author(s):  
Michael Penn ◽  
Christopher Sadowski ◽  
Gautam Webb
Keyword(s):  
Algebraic Structure ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Gram Matrix ◽  
Vertex Operator Algebras ◽  
Generators And Relations ◽  
The Third ◽  
Exact Sequences

This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices [Formula: see text] whose Gram matrix contains only non-negative entries. We develop further ideas originally presented by Calinescu, Lepowsky, and Milas to find presentations (generators and relations) of the principal subspace of a certain natural twisted module for the vertex operator algebra [Formula: see text]. We then use these presentations to construct exact sequences involving this principal subspace, which give a set of recursions satisfied by the multigraded dimension of the principal subspace and allow us to find the multigraded dimension of the principal subspace.

scholarly journals Non-Abelian U -duality for membranes

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Yuho Sakatani ◽  
Shozo Uehara
Keyword(s):  
String Theory ◽  
Isometry Group ◽  
Standard Treatment ◽  
Abelian Extension ◽  
Target Space ◽  
Membrane Theory ◽  
Drinfel’D Double ◽  
M Theory

Abstract The $T$-duality of string theory can be extended to the Poisson–Lie $T$-duality when the target space has a generalized isometry group given by a Drinfel’d double. In M-theory, $T$-duality is understood as a subgroup of $U$-duality, but the non-Abelian extension of $U$-duality is still a mystery. In this paper we study membrane theory on a curved background with a generalized isometry group given by the $\mathcal E_n$ algebra. This provides a natural setup to study non-Abelian $U$-duality because the $\mathcal E_n$ algebra has been proposed as a $U$-duality extension of the Drinfel’d double. We show that the standard treatment of Abelian $U$-duality can be extended to the non-Abelian setup. However, a famous issue in Abelian $U$-duality still exists in the non-Abelian extension.

scholarly journals A Locally Supersymmetric Action for the Scalar Particle

1997 ◽  
Vol 12 (18) ◽  
pp. 1291-1299
Author(s):  
Fiorenzo Bastianelli ◽  
Luca Consoli
Keyword(s):  
Gauge Symmetry ◽  
Algebraic Structure ◽  
Scalar Particle ◽  
Bosonic String ◽  
Invariant Action ◽  
Reparametrization Invariance

We construct a locally supersymmetric action for the scalar particle, and study its relation with the usual reparametrization invariant action. The mechanisms at work are similar to those employed in the embedding of the bosonic string into the fermionic one, originally due to Berkovits and Vafa in their search for a universal string. The simpler algebraic structure present in the particle case provides us with a guide on how to prove in a simple way, without the need of fixing the superconformal gauge, that the supersymmetric formulation of the bosonic string is equivalent to the usual one, where reparametrization invariance is the only worldsheet gauge symmetry.

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.

FIVEBRANE STRUCTURES

2009 ◽  
Vol 21 (10) ◽  
pp. 1197-1240 ◽  
Author(s):  
HISHAM SATI ◽  
URS SCHREIBER ◽  
JIM STASHEFF
Keyword(s):  
String Theory ◽  
Heterotic String ◽  
Target Space ◽  
Type Ii ◽  
Anomaly Cancellation ◽  
Heterotic String Theory ◽  
Dual Version ◽  
String Structure ◽  
Topological Obstructions ◽  
The One

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

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