Spontaneous breaking of spacetime symmetries and the inverse Higgs effect

The supergravity dual of the superconformal anomaly multiplet in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between an [Formula: see text]SU(N+M) × SU(N) supersymmetric gauge theory and type IIB superstring in a space–time background described by the Klebanov–Strassler solution. Based on the fact that fractional D3-branes lead to superconformal anomaly on the field theory side and in the meantime deform AdS 5 × T1, 1 space–time background on the gravity side, we observe the five-dimensional gauged supergravity yielded from the spontaneous compactification on the deformed T1, 1, and find that the spontaneous breaking of local symmetries and the consequent super-Higgs effect in the gauged AdS5 supergravity should be the dual of the superconformal anomaly of the four-dimensional supersymmetric gauge theory.

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A Simple Model of Speculation as a Spontaneous Breaking of Symmetry - The Welfare Analyses and Some Problems in the Decision Making Theory

SSRN Electronic Journal ◽

10.2139/ssrn.3431883 ◽

2019 ◽

Author(s):

Takaaki Aoki

Keyword(s):

Decision Making ◽

Simple Model ◽

Spontaneous Breaking

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Spacetime symmetries

10.1093/oso/9780198802877.003.0006 ◽

2018 ◽

Author(s):

Michael Kachelriess

Keyword(s):

Riemannian Manifold ◽

Conservation Laws ◽

Vector Fields ◽

Killing Vector ◽

Geodesic Equation ◽

Spacetime Symmetries ◽

Tensor Fields ◽

Killing Vector Fields ◽

Covariant Derivatives ◽

Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

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Nilpotent symmetries as a mechanism for Grand Unification

Journal of High Energy Physics ◽

10.1007/jhep05(2021)240 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Lars Andersson ◽

András László ◽

Błażej Ruba

Keyword(s):

Gauge Field ◽

Scalar Product ◽

Local Symmetry ◽

Matter Field ◽

Gauge Fields ◽

Spacetime Symmetries ◽

Invariant Scalar ◽

Spacetime Manifold ◽

Local Symmetries ◽

Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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Symmetry breaking at high temperatures in large N gauge theories

Journal of High Energy Physics ◽

10.1007/jhep08(2021)148 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Soumyadeep Chaudhuri ◽

Eliezer Rabinovici

Keyword(s):

Fixed Point ◽

Phase Transitions ◽

Symmetry Breaking ◽

High Temperatures ◽

Gauge Theories ◽

Scalar Fields ◽

Temperature Limit ◽

Spontaneous Breaking ◽

Critical Temperatures ◽

Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

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