scholarly journals THE OSp(32|1) VERSUS OSp(8|2) SUPERSYMMETRIC M-BRANE ACTION FROM SELF-DUAL (2, 2) STRINGS

1996 ◽  
Vol 11 (29) ◽  
pp. 2369-2379 ◽  
Author(s):  
SERGEI V. KETOV
Keyword(s):  
Lorentz Invariance ◽  
Target Space ◽  
Higher Dimensional ◽  
Starting Point ◽  
Symmetry Structure ◽  
String Membrane ◽  
M Theory ◽  
Chern Simons ◽  
Integrable Field ◽  
Fundamental Formulation

Taking the (2, 2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the “Lorentz” invariance and supersymmetry in the (2, 2) string target space leads to an extension of the (2, 2) string theory to a theory of (2+2)-dimensional supermembranes (M-branes) propagating in a higher-dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the “Lorentz” covariance and dimensional reasons. The Kähler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp (32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.

scholarly journals EMBEDDING FRACTIONAL QUANTUM HALL SOLITONS IN M-THEORY COMPACTIFICATIONS

2011 ◽  
Vol 08 (07) ◽  
pp. 1507-1518 ◽  
Author(s):  
A. BELHAJ ◽  
N.-E. FAHSSI ◽  
E. H. SAIDI ◽  
A. SEGUI
Keyword(s):  
Quantum Hall ◽  
Target Space ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hirzebruch Surfaces ◽  
Dynkin Diagrams ◽  
Higher Dimensional ◽  
Dynkin Quivers ◽  
M Theory ◽  
Chern Simons

We engineer U(1)n Chern–Simons type theories describing fractional quantum Hall solitons (QHS) in 1 + 2 dimensions from M-theory compactified on eight-dimensional hyper-Kähler manifolds as target space of N = 4 sigma model. Based on M-theory/type IIA duality, the systems can be modeled by considering D6-branes wrapping intersecting Hirzebruch surfaces F0's arranged as ADE Dynkin Diagrams and interacting with higher-dimensional R-R gauge fields. In the case of finite Dynkin quivers, we recover well known values of the filling factor observed experimentally including Laughlin, Haldane and Jain series.

scholarly journals 6d $$ \mathcal{N} $$ = (1, 0) anomalies on S1 and F-theory implications

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Pierre Corvilain
Keyword(s):  
Lorentz Invariance ◽  
Perfect Match ◽  
Gauge Coupling ◽  
Theory Reduction ◽  
Free Theory ◽  
Field Dependent ◽  
Gauge Anomalies ◽  
Effective Theories ◽  
M Theory ◽  
Chern Simons

Abstract We show that the pure gauge anomalies of 6d $$ \mathcal{N} $$ N = (1, 0) theories compactified on a circle are captured by field-dependent Chern-Simons terms appearing at one-loop in the 5d effective theories. These terms vanish if and only if anomalies are canceled. In order to obtain this result, it is crucial to integrate out the massive Kaluza-Klein modes in a way that preserves 6d Lorentz invariance; the often-used zeta-function regularization is not sufficient. Since such field-dependent Chern-Simons terms do not arise in the reduction of M-theory on a threefold, six-dimensional F-theory compactifications are automatically anomaly free, whenever the M/F-duality can be used. A perfect match is then found between the 5d $$ \mathcal{N} $$ N = 1 prepotentials of the classical M-theory reduction and one-loop circle compactification of an anomaly free theory. Finally, from this potential, we read off the quantum corrections to the gauge coupling functions.

scholarly journals TENSORIAL CENTRAL CHARGES AND NEW SUPERPARTICLE MODELS WITH FUNDAMENTAL SPINOR COORDINATES

1999 ◽  
Vol 14 (19) ◽  
pp. 1257-1272 ◽  
Author(s):  
IGOR BANDOS ◽  
JERZY LUKIERSKI
Keyword(s):  
Degrees Of Freedom ◽  
Lorentz Invariance ◽  
Target Space ◽  
Grassmann Variable ◽  
Massless Case ◽  
Higher Dimensional

We consider firstly simple D=4 superalgebra with six real tensorial central charges Zμν, and discuss its possible realizations in massive and massless cases. Massless case is dynamically realized by generalized Ferber–Shirafuji (FS) model with fundamental bosonic spinor coordinates. The Lorentz invariance is not broken due to the realization of central charges generators in terms of bosonic spinors. The model contains four fermionic coordinates and possesses three κ-symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (eight real bosonic and one real Grassmann variable) of our model can be described by OSp (8|1) supertwistor. The relation with recent superparticle model by Rudychev and Sezgin is pointed out. Finally we propose a higher-dimensional generalization of our model with one real fundamental bosonic spinor. D=10 model describes massless superparticle with composite tensorial central charges and in D=11 we obtain zero-superbrane model with nonvanishing mass which is generated dynamically.

scholarly journals A HIGHER CHERN–WEIL DERIVATION OF AKSZ σ-MODELS

2012 ◽  
Vol 10 (01) ◽  
pp. 1250078 ◽  
Author(s):  
DOMENICO FIORENZA ◽  
CHRISTOPHER L. ROGERS ◽  
URS SCHREIBER
Keyword(s):  
Lie Algebras ◽  
Symplectic Manifold ◽  
Target Space ◽  
Simons Theory ◽  
Invariant Polynomial ◽  
Action Functional ◽  
Higher Dimensional ◽  
The Given ◽  
Chern Simons ◽  
Chern Simons Theory

Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-connections to differential cocycles whose volume holonomy is the corresponding Chern–Simons theory action functional. Kotov and Strobl have observed that this naturally generalizes from Lie algebras to dg-manifolds and to dg-bundles and that the Chern–Simons action functional associated this way to an n-symplectic manifold is the action functional of the AKSZ σ-model whose target space is the given n-symplectic manifold (examples of this are the Poisson σ-model or the Courant σ-model, including ordinary Chern–Simons theory, or higher-dimensional Abelian Chern–Simons theory). Here we show how, within the framework of the higher Chern–Weil theory in smooth ∞-groupoids, this result can be naturally recovered and enhanced to a morphism of higher stacks, the same way as ordinary Chern–Simons theory is enhanced to a morphism from the stack of principal G-bundles with connections to the 3-stack of line 3-bundles with connections.

scholarly journals The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Damon J. Binder ◽  
Shai M. Chester ◽  
Max Jerdee ◽  
Silviu S. Pufu
Keyword(s):  
Block Decomposition ◽  
Point Function ◽  
Present Evidence ◽  
Bootstrap Techniques ◽  
Wide Range ◽  
Higher Spin ◽  
Tensor Multiplet ◽  
Higher Spins ◽  
M Theory ◽  
Chern Simons

Abstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

scholarly journals M2-BRANES AND AdS/CFT

2010 ◽  
Vol 25 (02n03) ◽  
pp. 332-350 ◽  
Author(s):  
IGOR R. KLEBANOV
Keyword(s):  
Abjm Theory ◽  
Dual Formulation ◽  
Matter Theory ◽  
Monopole Operators ◽  
M Theory ◽  
Chern Simons

We provide a brief introduction to the ABJM theory, the level kU(N) × U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2 -branes. We discuss its dual formulation in terms of M -theory on AdS4 × S7/ℤk and review some of the evidence in favor of the conjecture. We end with a brief discussion of the important role played by the monopole operators.

scholarly journals A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Grand Unification ◽  
De Sitter ◽  
Sitter Group ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
M Theory ◽  
Chern Simons ◽  
Topological Part ◽  
Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

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.

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