scholarly journals On a gravity dual to flavored topological quantum mechanics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrey Feldman
Keyword(s):  
Quantum Mechanics ◽  
Effective Field ◽  
Abjm Theory ◽  
Yang Mills ◽  
Topological Quantum ◽  
Higher Derivatives ◽  
Structure Constants ◽  
Holographic Description ◽  
M Theory ◽  
Chern Simons

Abstract In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $$ \mathcal{N} $$ N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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 Superconformal Line Defects in 3D

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 348
Author(s):  
Silvia Penati
Keyword(s):  
Three Dimensional ◽  
Fundamental Relation ◽  
Abjm Theory ◽  
Superconformal Field Theories ◽  
Conformal Bootstrap ◽  
Topological Quantum ◽  
Exact Evaluation ◽  
Line Defects ◽  
Chern Simons ◽  
Physical Quantities

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.

scholarly journals D-Brane Configurations and Nicolai Map in Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (03) ◽  
pp. 183-193 ◽  
Author(s):  
I. I. Kogan ◽  
R. J. Szabo ◽  
G. W. Semenoff
Keyword(s):  
Quantum Mechanics ◽  
Phase Transitions ◽  
Matrix Model ◽  
Short Distance ◽  
Dimensional Theory ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
M Theory ◽  
Matrix Quantum

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang–Mills theory in 10 dimensions and which has been recently argued to represent the short-distance structure of M-theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full 11-dimensional theory.

CHERN-SIMONS QUANTUM MECHANICS, SUPERSYMMETRY, AND SYMPLECTIC INVARIANTS

1991 ◽  
Vol 06 (03) ◽  
pp. 365-379 ◽  
Author(s):  
MATTHIAS BLAU
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Explicit Calculation ◽  
Infinite Dimensions ◽  
Conformal Field ◽  
Mechanics Model ◽  
Topological Quantum ◽  
Symplectomorphism Group ◽  
Symplectic Invariants ◽  
Chern Simons

We explain the relation between supersymmetry and equivariant cohomology, combining recent investigations of Chern-Simons quantum mechanics and path integrals on coadjoint orbits. We then construct a supersymmetric (topological) quantum mechanics model whose partition function — probing the cohomology of the symplectomorphism group — yields a symplectic invariant introduced by Weinstein. We demonstrate by explicit calculation that this provides another example where the Duistermaat-Heckman theorem (exactness of the semi-classical approximation) appears to hold in infinite dimensions, and make some suggestions concerning its role in (conformal) field theory.

FUSION RULES, TOPOLOGICAL QUANTUM MECHANICS AND THREE-MANIFOLDS

1993 ◽  
Vol 08 (31) ◽  
pp. 3001-3010 ◽  
Author(s):  
JUAN MATEOS GUILARTE
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Hamiltonian Formalism ◽  
Fusion Rules ◽  
Path Integral Quantization ◽  
Topological Quantum ◽  
Verlinde Algebra ◽  
Chern Simons

Path-integral quantization of Chern-Simons field theory in the Hamiltonian formalism is developed. A derivation of Verlinde algebra in topological quantum mechanics arises and three-manifold invariants are recovered.

BRAID STATISTICS FOR THE SOURCES OF THE NONABELIAN CHERN-SIMONS TERM

1990 ◽  
Vol 05 (12) ◽  
pp. 2423-2470 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. BOURDEAU ◽  
S. JO
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Point Particle ◽  
Yang Mills ◽  
Direct Sum ◽  
Identical Point ◽  
Effective Lagrangian ◽  
All Solutions ◽  
Chern Simons

A Lagrangian consisting of an Abelian Chern-Simons term and N identical point particle sources is known to lead to fractional statistics for the sources. In this paper, we investigate the non-Abelian generalization of this system with special emphasis on source statistics. All solutions for the Yang-Mills potential in the presence of identical or nonidentical sources are found. For two or more sources, they fall in many gauge inequivalent classes whereas in the Abelian problem, there is only one such class. An effective Lagrangian for N sources is found for each of these solutions. The quantum mechanics and statistics of the sources are sensitive to the potential leading to the effective Lagrangian. There is for instance, a class of solutions for identical sources which are not invariant under exchange of sources. For these solutions, the identity of the sources obliges us to consider such a potential and all its exchange transforms at the same time, and to introduce a Hilbert space of states which is the direct sum of the Hilbert spaces associated with each of these potentials. There are also exchange invariant potentials for identical sources. For SU(3) and N = 3, all exchange invariant potentials are shown to lead to statistics defined by S3 representations. The nature of statistics for SU (M) for higher M as also the creation of intrinsic spin by self interaction are briefly considered.

scholarly journals Witten effect, anomaly inflow, and charge teleportation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hajime Fukuda ◽  
Kazuya Yonekura
Keyword(s):  
Quantum Mechanics ◽  
Magnetic Monopole ◽  
Charged Particles ◽  
Magnetic Monopoles ◽  
Three Dimensions ◽  
Total Charge ◽  
Four Dimensions ◽  
Linking Number ◽  
M Theory ◽  
Chern Simons

Abstract We study a phenomenon that electric charges are “teleported” between two spatially separated objects without exchanging charged particles at all. For example, this phenomenon happens between a magnetic monopole and an axion string in four dimensions, two vortices in three dimensions, and two M5-branes in M-theory in which M2-charges are teleported. This is realized by anomaly inflow into these objects in the presence of cubic Chern-Simons terms. In particular, the Witten effect on magnetic monopoles can be understood as a general consequence of anomaly inflow, which implies that some anomalous quantum mechanics must live on them. Charge violation occurs in the anomalous theories living on these objects, but it happens in such a way that the total charge is conserved between the two spatially separated objects. We derive a formula for the amount of the charge which is teleported between the two objects in terms of the linking number of their world volumes in spacetime.

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