scholarly journals AdS3 from M-branes at conical singularities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Giuseppe Dibitetto ◽  
Nicolò Petri
Keyword(s):  
Riemann Surface ◽  
Equations Of Motion ◽  
Conical Singularities ◽  
General Solutions ◽  
Deficit Angle ◽  
Conical Defect ◽  
M Theory

Abstract M-theory is known to possess supersymmetric solutions where the geometry is AdS3 × S3 × S3 warped over a Riemann surface Σ2. The simplest examples in this class can be engineered by placing M2 and M5 branes as defects inside of a stack of background M5 branes. In this paper we show that a generalization of this construction yields more general solutions in the aforementioned class. The background branes are now M5’s carrying M2 brane charge, while the defect branes are now placed at the origin of a flat hyperplane with a conical defect. The equations of motion imply a relation between the deficit angle produced by the conical defect and the M2 charge carried by the background branes.

scholarly journals SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM

2001 ◽  
Vol 16 (05) ◽  
pp. 822-855 ◽  
Author(s):  
JUAN MALDACENA ◽  
CARLOS NUÑEZ
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Field Theories ◽  
De Sitter ◽  
Curved Manifolds ◽  
Conformal Field ◽  
Low Energies ◽  
M Theory

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form Rd×Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS5. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

scholarly journals Current algebra formulation of M-theory based on E11 Kac–Moody algebra

2017 ◽  
Vol 32 (05) ◽  
pp. 1750024 ◽  
Author(s):  
Hirotaka Sugawara
Keyword(s):  
Current Algebra ◽  
Equations Of Motion ◽  
Internal Symmetry ◽  
Momentum Tensor ◽  
Moody Algebra ◽  
Finite Dimensional ◽  
The One ◽  
Quantum Equations ◽  
M Theory ◽  
Gravitino Field

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac–Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the [Formula: see text] Kac–Moody algebra that was shown recently[Formula: see text] to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside [Formula: see text], so that, by constructing the current algebra of [Formula: see text], I obtain both internal gauge theory and gravity theory. The energy–momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein–Hilbert action.

scholarly journals Higher-derivative supergravity, AdS4 holography, and black holes

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Nikolay Bobev ◽  
Anthony M. Charles ◽  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Black Holes ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Conformal Supergravity ◽  
Supergravity Theory ◽  
Higher Derivative ◽  
All Solutions ◽  
M Theory ◽  
Supergravity Action

Abstract We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $$ \mathcal{N} $$ N = 2 gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS4 solution of the two-derivative equations of motion. The four-derivative terms in the supergravity Lagrangian modify the entropy and other thermodynamic observables for the black hole solutions of the theory. We calculate these corrections explicitly and demonstrate that the quantum statistical relation holds for general stationary black holes in the presence of the four-derivative corrections. Employing an embedding of this supergravity model in M-theory we show how to use supersymmetric localization results in the holographically dual three-dimensional SCFT to determine the unknown coefficients in the four-derivative supergravity action. This in turn leads to new detailed results for the first subleading $$ {N}^{\frac{1}{2}} $$ N 1 2 correction to the large N partition function of a class of three-dimensional SCFTs on compact Euclidean manifolds. In addition, we calculate explicitly the first subleading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes in M-theory. We also discuss how to add matter multiplets to the supergravity theory in the presence of four-derivative terms and to generalize some of these results to six- and higher-derivative supergravity.

On the Unified General Solutions of Linear Wave Motions of Thermoelastodynamics and Hydrodynamics With Practical Examples

1967 ◽  
Vol 34 (4) ◽  
pp. 879-887 ◽  
Author(s):  
P. K. Wong
Keyword(s):  
Equations Of Motion ◽  
Viscous Fluids ◽  
Linear Wave ◽  
Elastic Solids ◽  
Cylindrical Coordinates ◽  
General Solutions ◽  
The Media ◽  
Systematic Solution ◽  
Thermally Conducting ◽  
Wave Problems

In analogy to the development of the potential equations of motion of linear elastodynamics, the governing potential equations for linear wave motions of hydrodynamics and thermoelastodynamics are systematically exploited. As a result of these developments, problems of linear wave motions of homogeneous, isotropic, thermally conducting multi-layered elastic solids and viscous fluids can be systematically solved for the media whose boundaries are described by rectangular, circular, parabolic, and elliptic cylindrical coordinates, as well as by spherical and conical coordinates. Five practical examples are analytically solved to illustrate how the use of the potential equations of motion leads to more systematic solution procedures; these examples can be used for the modeling studies of aero and hydrospace vehicles, geological wave problems, and macroscopic biomechanics.

scholarly journals ON FAIRLIE'S MOYAL FORMULATION OF M(ATRIX)-THEORY

2001 ◽  
Vol 16 (31) ◽  
pp. 4969-4984
Author(s):  
M. HSSAINI ◽  
M. B. SEDRA ◽  
M. BENNAI ◽  
B. MAROUFI
Keyword(s):  
Poisson Bracket ◽  
Explicit Form ◽  
Simple Form ◽  
Equations Of Motion ◽  
Yang Mills ◽  
First Order ◽  
Large N ◽  
Special Cases ◽  
M Theory ◽  
Conserved Currents

Starting from the Moyal formulation of M theory in the large N-limit, we propose to reexamine the associated membrane equations of motion in ten dimensions formulated in terms of Poisson bracket. Among the results obtained, we rewrite the coupled first order Nahm equations into a simple form leading in turn to their systematic relation with SU (∞) Yang–Mills equations of motion. The former are interpreted as the vanishing condition of some conserved currents which we propose. We develop also an algebraic analysis in which an ansatz is considered and find an explicit form for the membrane solution of our problem. Typical solutions known in literature can also emerge as special cases of the proposed solution.

scholarly journals REMARKS ON E11 APPROACH

2006 ◽  
Vol 21 (06) ◽  
pp. 503-514
Author(s):  
H. MKRTCHYAN ◽  
R. MKRTCHYAN
Keyword(s):  
Equations Of Motion ◽  
Coadjoint Orbits ◽  
Square Root ◽  
Fundamental Representation ◽  
Self Duality ◽  
Particle Orbit ◽  
M Theory

We consider a few topics in E11 approach to superstrings/M-theory: even subgroups (Z2 orbifolds) of En, n = 11, 10, 9 and their connection to Kac–Moody algebras, particularly to EE11 subgroup of E11; possible form of supersymmetry relation in E11; decomposition of first fundamental representation l1 w.r.t. the SO (10, 10) and its square-root at first few levels; particle orbit of l1 ⋉ E11. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in E11.

scholarly journals Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces

2017 ◽  
Vol 2017 (724) ◽  
Author(s):  
Hiroshi Isozaki ◽  
Yaroslav Kurylev ◽  
Matti Lassas
Keyword(s):  
Inverse Problem ◽  
Riemann Surface ◽  
Inverse Scattering ◽  
Scattering Matrix ◽  
Hyperbolic Surfaces ◽  
Conical Singularities ◽  
Compact Surfaces ◽  
Asymptotically Hyperbolic ◽  
Generalized Scattering Matrix

AbstractWe consider an inverse problem associated with some 2-dimensional non-compact surfaces with conical singularities, cusps and regular ends. Our motivating example is a Riemann surface

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