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.

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 Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals The “Emerging” Reality from “Hidden” Spaces

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 75
Author(s):  
Richard Pincak ◽  
Alexander Pigazzini ◽  
Saeid Jafari ◽  
Cenap Ozel
Keyword(s):  
Dark Matter ◽  
String Theory ◽  
Topological Approach ◽  
New Approach ◽  
Topological Interpretation ◽  
New Interpretation ◽  
M Theory

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole, but mainly we provide a topological interpretation, using this new approach, to M-Theory and String Theory in 10 dimensions. Further, we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the “emerging” part of a more complex hidden structure. Pacs numbers: 11.25.Yb; 11.25.-w; 02.40.Ky; 02.40.-k; 04.50.-h; 95.35.+d.

scholarly journals 5d and 4d SCFTs: canonical singularities, trinions and S-dualities

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Cyril Closset ◽  
Simone Giacomelli ◽  
Sakura Schäfer-Nameki ◽  
Yi-Nan Wang
Keyword(s):  
String Theory ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Crepant Resolution ◽  
Superconformal Field Theories ◽  
Hypersurface Singularities ◽  
Canonical Singularities ◽  
Type Iib String Theory ◽  
M Theory

Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

scholarly journals The Fayet-Iliopoulos term in Type-I string theory and M-theory

1998 ◽  
Vol 437 (3-4) ◽  
pp. 318-324 ◽  
Author(s):  
John March-Russell
Keyword(s):  
String Theory ◽  
Type I ◽  
M Theory

scholarly journals SOME COMMENTS ON BRANES, G-FLUX, AND K-THEORY

2001 ◽  
Vol 16 (05) ◽  
pp. 936-944 ◽  
Author(s):  
GREGORY MOORE
Keyword(s):  
String Theory ◽  
K Theory ◽  
M Theory

Summary of a talk explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.

scholarly journals FROM p-BRANES TO COSMOLOGY

1999 ◽  
Vol 14 (26) ◽  
pp. 4121-4142 ◽  
Author(s):  
H. LÜ ◽  
S. MUKHERJI ◽  
C. N. POPE
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Cosmological Models ◽  
Cosmological Solutions ◽  
M Theory ◽  
The Relationship

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M theory. We discuss two different ways in which extremal p-branes can be generalized to nonextremal ones, and show how wide classes of recently discussed cosmological models can be mapped into nonextremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalized dimensional reduction of string theory or M theory.

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 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.

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