scholarly journals Dyons, Superstrings, and Wormholes: Exact Solutions of the Non-Abelian Dirac-Born-Infeld Action

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Edward A. Olszewski
Keyword(s):  
Gravitational Interaction ◽  
Spatial Dimension ◽  
Adjoint Representation ◽  
Type I ◽  
Superstring Theory ◽  
Duality Transformation ◽  
Yang Mills ◽  
Dimensional Spacetime ◽  
Lorentz Scalar ◽  
Gauge Gravity

We construct dyon solutions on coincidentD4-branes, obtained by applyingT-duality transformations to type ISO(32)superstring theory in 10 dimensions. These solutions, which are exact, are obtained from an action comprising the non-Abelian Dirac-Born-Infeld action and a Wess-Zumino-like action. When one spatial dimension of theD4-branes is taken to be vanishingly small, the dyons are analogous to the ’t Hooft/Polyakov monopole residing in a3+1-dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is reinterpreted as a Higgs boson transforming in the adjoint representation of the gauge group. Applying aT-duality transformation to the vanishingly small spatial dimension, we obtain a collection ofD3-branes, not all of which are coincident. Two of theD3-branes, distinct from the others, acquire intrinsic, finite curvature and are connected by a wormhole. The dyons possess electric and magnetic charges whose values on eachD3-brane are the negative of one another. The gravitational effects, which arise after theT-duality transformation, occur despite the fact that the action of the system does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, that is, gauge/gravity duality.

scholarly journals Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Yasuhiro Sekino
Keyword(s):  
Gauge Theory ◽  
Free Field ◽  
Scalar Fields ◽  
Superstring Theory ◽  
Spatial Direction ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Brane Solution ◽  
Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

scholarly journals DUALITY AND COSMOLOGICAL COMPACTIFICATION OF SUPERSTRINGS WITH UNBROKEN SUPERSYMMETRY

1999 ◽  
Vol 14 (07) ◽  
pp. 1035-1047
Author(s):  
H. K. JASSAL ◽  
A. MUKHERJEE ◽  
R. P. SAXENA
Keyword(s):  
Scale Factor ◽  
Initial Singularity ◽  
Superstring Theory ◽  
Duality Transformation ◽  
Yang Mills ◽  
Consistency Conditions ◽  
Cosmological Solutions ◽  
Super Yang Mills Theory

The cosmological compactification of D=10, N=1 supergravity–super-Yang–Mills theory obtained from superstring theory is studied. The constraint of unbroken N=1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontrivial scale factor and a dynamical dilaton. It is shown that various classes of solutions are possible, which include cosmological solutions with no initial singularity.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Eisenstein Series ◽  
Mass Parameter ◽  
Flat Space ◽  
Superstring Theory ◽  
Modular Invariant ◽  
Yang Mills ◽  
Laplace Eigenvalue ◽  
Modular Invariants ◽  
Tensor Multiplet ◽  
Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

scholarly journals MAXIMALLY SYMMETRIC MINIMAL UNIFICATION MODEL SO(32) WITH THREE FAMILIES IN TEN-DIMENSIONAL SPACETIME

2007 ◽  
Vol 22 (04) ◽  
pp. 259-271 ◽  
Author(s):  
YUE-LIANG WU
Keyword(s):  
Gauge Symmetry ◽  
Correspondence Principle ◽  
Quantum Spin ◽  
Spinor Representation ◽  
Type I ◽  
Weyl Spinor ◽  
Spinor Structure ◽  
Dimensional Spacetime ◽  
Quantum Spacetime ◽  
Quantum Charge

Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana–Weyl spinor representation of 14 dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra six dimensions that relate to quantum family charges. Of particular, it is shown that ten dimensions relating to quantum spin-family charges form a motional ten-dimensional quantum spacetime with a generalized Lorentz symmetry SO (1, 9), and ten dimensions relating to quantum isospin-color charges become a motionless ten-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO (32). As a consequence, a maximally symmetric minimal unification model SO (32) containing three families in ten-dimensional quantum spacetime is naturally obtained by choosing a suitable Majorana–Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with those of type I string and heterotic string SO (32) in string theory.

scholarly journals Dirac operators with Lorentz scalar shell interactions

2018 ◽  
Vol 30 (05) ◽  
pp. 1850013 ◽  
Author(s):  
Markus Holzmann ◽  
Thomas Ourmières-Bonafos ◽  
Konstantin Pankrashkin
Keyword(s):  
Dirac Operator ◽  
Spectral Properties ◽  
Smooth Surface ◽  
Three Dimensional ◽  
The Self ◽  
Eigenvalue Asymptotics ◽  
Yang Mills ◽  
Lorentz Scalar ◽  
Definition Of ◽  
The Individual

This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.

scholarly journals Exact Solutions in Poincaré Gauge Gravity Theory

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 127 ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Gravitational Field ◽  
Gravity Models ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Yang Mills ◽  
Gravitational Field Equations ◽  
Poincaré Symmetry ◽  
Gauge Gravity ◽  
Vacuum Solutions

In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

scholarly journals Testing the holographic principle using lattice simulations

2018 ◽  
Vol 175 ◽  
pp. 08004 ◽  
Author(s):  
Raghav G. Jha ◽  
Simon Catterall ◽  
David Schaich ◽  
Toby Wiseman
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Strong Coupling ◽  
Type Ii ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Made In

The lattice studies of maximally supersymmetric Yang-Mills (MSYM) theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory–Laflamme) between them.

scholarly journals DUALITY TRANSFORMATION FOR (3+1)-DIMENSIONAL YANG–MILLS THEORY

2002 ◽  
Vol 17 (02) ◽  
pp. 175-186
Author(s):  
PUSHAN MAJUMDAR ◽  
H. S. SHARATCHANDRA
Keyword(s):  
Gauge Theory ◽  
Canonical Transformation ◽  
Dual Theory ◽  
Duality Transformation ◽  
Yang Mills ◽  
Dual Form

A dual form of (3+1)-dimensional Yang–Mills theory is obtained as another SO(3) gauge theory. Duality transformation is realized as a canonical transformation. The non-Abelian Gauss law implies the corresponding Gauss law for the dual theory. The dual theory is nonlocal. There is a nonlocal version of Yang–Mills theory which is self-dual.

scholarly journals WARPED SELF-GRAVITATING U(1) GAUGE COSMIC STRINGS IN 5D

2012 ◽  
Vol 21 (07) ◽  
pp. 1250060 ◽  
Author(s):  
REINOUD JAN SLAGTER ◽  
DERK MASSELINK
Keyword(s):  
Numerical Solutions ◽  
Cosmic Strings ◽  
Unit Length ◽  
Planck Scale ◽  
Brane World ◽  
Energy Tensor ◽  
Axially Symmetric ◽  
Superstring Theory ◽  
Dimensional Spacetime ◽  
Gut Scale

We present the "classical" Nielsen–Olesen vortex solution on a warped 5-dimensional spacetime, where we solved the effective 4-dimensional equations from the 5-dimensional equations together with the junction and boundary conditions. 4-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, Gμ ≤ 10-6. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings (Gμ ≳ 1), predicted by superstring theory, possess some problems. They are studied because the universe may have undergone phase transitions at scales much higher than the GUT scale. But Gμ ≳ 1 is far above observational bounds, so one needs an inflationary scenario to smooth them out. Further, it is believed that these super-massive strings never extended to macroscopic size. Brane world models could overcome these problems. Gμ could be warped down to GUT scale, even if its value was at the Planck scale. In our warped cosmic string model, where the string mass per unit length in the bulk can be of order of the Planck scale, we find that the 4-dimensional brane spacetime is exponential warped down. Moreover, asymptotically the induced 4-dimensional spacetime does not show conical behavior. So there is no angle deficit compared to its value in the bulk and the spacetime seems to be unphysical, at least under fairly weak assumptions on the stress–energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations.

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