scholarly journals Wrapped NS5-branes, consistent truncations and Inönü-Wigner contractions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
K. C. Matthew Cheung ◽  
Rahim Leung
Keyword(s):  
Gauge Group ◽  
Discrete Group ◽  
Vector Multiplet ◽  
Consistent Truncations ◽  
Group Of Symmetries ◽  
Lower Dimensional ◽  
Kaluza Klein

Abstract We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) Σ2 × S3 and (ii) Σ3 × S3, where Σ2 = S2/Γ, ℝ2/Γ, or ℍ2/Γ, and Σ3 = S3/Γ, ℝ3/Γ, or ℍ3/Γ, with Γ a discrete group of symmetries, corresponding to NS5-branes wrapped on Σ2 and Σ3. The resulting theories are a D = 5, $$ \mathcal{N} $$ N = 4 gauged supergravity coupled to three vector multiplets with scalar manifold SO(1, 1) × SO(5, 3)/(SO(5) × SO(3)) and gauge group SO(2) × (SO(2) $$ {\ltimes}_{\Sigma_2} $$ ⋉ Σ 2 ℝ4) which depends on the curvature of Σ2, and a D = 4, $$ \mathcal{N} $$ N = 2 gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold SU(1, 1)/U(1) × G2(2)/SO(4) and gauge group ℝ+ × ℝ+ for truncations (i) and (ii) respectively. Instead of carrying out the truncations at the 10-dimensional level, we show that they can be obtained directly by performing Inönü-Wigner contractions on the 5 and 4-dimensional gauged supergravity theories that come from consistent truncations of 11-dimensional supergravity associated with M5-branes wrapping Σ2 and Σ3. This suggests the existence of a broader class of lower-dimensional gauged supergravity theories related by group contractions that have a 10 or 11-dimensional origin.

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

scholarly journals KALUZA–KLEIN DIMENSIONAL REDUCTION AND GAUSS–CODAZZI–RICCI EQUATIONS

2009 ◽  
Vol 24 (06) ◽  
pp. 1207-1220
Author(s):  
PEI WANG
Keyword(s):  
General Relativity ◽  
Dimensional Reduction ◽  
Traditional Method ◽  
Isometry Group ◽  
Extrinsic Curvature ◽  
Internal Space ◽  
Geometric Meaning ◽  
Reduced Dimensions ◽  
Lower Dimensional ◽  
Kaluza Klein

In this paper we imitate the traditional method which is used customarily in the general relativity and some mathematical literatures to derive the Gauss–Codazzi–Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower-dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza–Klein gauge field strength. For isometry group of internal space, the SO (n) symmetry and SU (n) symmetry are discussed. And the Kaluza–Klein instanton is also enquired.

scholarly journals Examples of Calabi-Yau threefolds with small Hodge numbers

2021 ◽  
Vol 2081 (1) ◽  
pp. 012030
Author(s):  
A O Shishanin
Keyword(s):  
Fixed Point ◽  
Fundamental Group ◽  
Gauge Group ◽  
Complete Intersection ◽  
Euler Characteristic ◽  
Discrete Group ◽  
Free Action ◽  
Discrete Groups ◽  
Hodge Numbers ◽  
Fixed Point Sets

Abstract We observe some suitable examples of Calabi-Yau threefolds for heterotic superstring compactifications. It is reasonable to seek CY threefolds with Euler characteristic equals ±6 because of generation’s number. Hosotani mechanism for violations of the gauge group by the Wilson loops requires such CY space has a non-trivial fundamental group. These spaces can be obtained by factoring the complete intersection Calabi-Yau spaces by the free action of some discrete group. Also we shortly discuss cases when discrete groups act with fixed point sets.

scholarly journals Cosmic cloaking of rich extra dimensions

2021 ◽  
Author(s):  
Aghil Alaee ◽  
Marcus Khuri ◽  
Hari Kunduri
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Extra Dimensions ◽  
Large Extra Dimensions ◽  
Dimensional Theory ◽  
Hoop Conjecture ◽  
Significant Size ◽  
The Universe ◽  
Lower Dimensional ◽  
Kaluza Klein

We present arguments that show why it is difficult to see rich extra dimensions in the universe. Conditions are found where significant size and variation of the extra dimensions in a Kaluza–Klein compactification lead to a black hole in the lower-dimensional theory. The idea is based on the hoop conjecture concerning black hole existence, as well as on the observation that dimensional reduction on macroscopically large, twisted, or highly dynamical extra dimensions contributes positively to the energy density in the lower-dimensional theory and can induce gravitational collapse. A threshold for the size is postulated on the order of [Formula: see text][Formula: see text]m, whereby extra dimensions of length above this level must lie inside black holes, thus cloaking them from the view of outside observers. The threshold depends on the size of the universe, leading to speculation that in the early stages of evolution truly macroscopic and large extra dimensions would have been visible.

scholarly journals Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Sergei M. Kuzenko
Keyword(s):  
Gauge Group ◽  
Nonlinear Theory ◽  
Effective Action ◽  
Low Energy ◽  
Vector Multiplet ◽  
Coulomb Branch ◽  
Conformal Supergravity ◽  
Yang Mills ◽  
Planar Part ◽  
Invariant Coupling

Abstract We present $$ \mathcal{N} $$ N = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

scholarly journals Symmetries of the self-dual Yang-Mills equations

1994 ◽  
Vol 49 (1) ◽  
pp. 151-158
Author(s):  
Rod Halburd
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Gauge Group ◽  
Finite Dimension ◽  
The Self ◽  
Partial Differential ◽  
Yang Mills ◽  
Master System ◽  
Group Of Symmetries ◽  
Conformal Symmetries

It has been conjectured by R. S. Ward that the self-dual Yang-Mills Equations (SDYMEs) form a “master system” in the sense that most known integrable ordinary and partial differential equations are obtainable as reductions. We systematically construct the group of symmetries of the SDYMEs on R4 with semisimple gauge group of finite dimension and show that this yields only the well known gauge and conformal symmetries.

scholarly journals CONSISTENT AXIAL-LIKE GAUGE FIXING ON HYPERTORI

1994 ◽  
Vol 09 (31) ◽  
pp. 2913-2926 ◽  
Author(s):  
EDWIN LANGMANN ◽  
MANFRED SALMHOFER ◽  
ALEX KOVNER
Keyword(s):  
Gauge Group ◽  
Discrete Group ◽  
Gauge Condition ◽  
Polyakov Loop ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Axial Gauge ◽  
Gauge Fixing ◽  
Gribov Copies

We analyze the Gribov problem for SU (N) and U (N) Yang–Mills fields on d-dimensional tori, d = 2, 3, …. We give an improved version of the axial gauge condition and find an infinite, discrete group [Formula: see text] where r = N − 1 and N for G = SU (N) and U (N) respectively, containing all gauge transformations compatible with that condition. This residual gauge group [Formula: see text] provides all Gribov copies for nondegenerate configurations in d = 2 and for those of them for which all winding numbers of the Wilson–Polyakov loop in one direction vanish in d ≥ 3. This shows that the space of gauge orbits is an orbifold. We derive this result both in the Lagrangian and in the Hamiltonian framework.

scholarly journals Non-Abelian gauge fields as components of gravity in the discretized Kaluza–Klein theory

2017 ◽  
Vol 32 (18) ◽  
pp. 1750095
Author(s):  
Ai Viet Nguyen ◽  
Tien Du Pham
Keyword(s):  
Gauge Group ◽  
Noncommutative Geometry ◽  
The Other ◽  
Gauge Fields ◽  
Strong Interactions ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
First Case ◽  
Klein Theory ◽  
Kaluza Klein

Discretized Kaluza–Klein theory in [Formula: see text] spacetime can be constructed based on the concepts of noncommutative geometry. In this paper, we show that it is possible to incorporate the non-Abelian gauge fields in this framework. The generalized Hilbert–Einstein action is gauge invariant only in two cases. In the first case, the gauge group must be Abelian on one sheet of spacetime and non-Abelian on the other one. In the second case, the gauge group must be the same on two sheets of spacetime. Actually, the theories of electroweak and strong interactions can fit into these two cases.

scholarly journals Vacua and exact solutions in lower-D limits of EGB

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Liang Ma ◽  
H. Lü
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Exact Solutions ◽  
The Other ◽  
Reality Condition ◽  
Bonnet Gravity ◽  
Cosmological Solutions ◽  
Scalar Hair ◽  
Lower Dimensional ◽  
Kaluza Klein

AbstractWe consider the action principles that are the lower dimensional limits of the Einstein–Gauss–Bonnet gravity via the Kaluza–Klein route. We study the vacua and obtain some exact solutions. We find that the reality condition of the theories may select one vacuum over the other from the two vacua that typically arise in Einstein–Gauss–Bonnet gravity. We obtain exact black hole and cosmological solutions carrying scalar hair, including scalar hairy BTZ black holes with both mass and angular momentum turned on. We also discuss the holographic central charges in the asymptotic AdS backgrounds.

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