Constrained gauge-gravity duality in three and four dimensions

Assimos, Thiago S.; Sobreiro, R. F.

doi:10.1140/epjc/s10052-019-7552-3

Cited by 5 publications

(11 citation statements)

References 54 publications

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“…The results in this section generalize some of the results in the seminal works of Achúcarro and Townsend [1] and of Witten [3] to the off-shell case as well as to the four-dimensional case. Moreover, they improve the results already obtained in [8].…”

Section: Nilpotencysupporting

confidence: 84%

“…In this section we discuss the results obtained in [8] in a more formal way. We will focus mainly in the three-dimensional Poincaré case for the CS gauge theory.…”

Section: Nilpotencymentioning

confidence: 99%

“…As discussed in [1,3,8], the analysis can be extended to the principal bundle P (SU (2) × S(3), M ) such that SO(4) ≡ SU (2) × S(3) with S(3) being pseudo-translations. The algebra is modified only for the translational sector, namely gauge symmetry, the constraints to be demanded are now [8] i X Ω ij − Λ 2 e i e j = 0 ,…”

Section: Three-dimensional Orthogonal Chern-simons Theorymentioning

confidence: 99%

“…A few of decades after the seminal papers [1,3], in [8], we have extended their gauge-gravity equivalence (GGE) analysis in two ways: First, we were able to abolish the need of the field equations, performing an off-shell generalization. The price we paid for that is to deal with a pair of constraints over curvature and torsion 2-forms.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work we review the results of [8] within a formal mathematical apparatus. First, the physical and mathematical structures of the GGE is extensively exploited under the eyes of fiber bundle theory [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Topological gauge-gravity equivalence: fiber bundle and homology aspects

Assimos¹,

Sobreiro²

2021

Preprint

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In the works of A. Achúcarro and P. K. Townsend and also by E. Witten, a duality between threedimensional Chern-Simons gauge theories and gravity was established. First (Achúcarro and Townsend), by considering an Inönü-Wigner contraction from a superconformal gauge theory to an Anti-de Sitter supergravity. Then, Witten was able to obtain, from Chern-Simons theory (in two cases: Poincaré and de Sitter gauge theories), an Einstein-Hilbert gravity by mapping the gauge symmetry in local isometries and diffeomorphisms. In all cases, the results made use of the field equations. Latter, we were capable to generalize Witten's work (in Euclidean spacetime) to the off-shell cases, as well as to four dimensional Yang-Mills theory with de Sitter gauge symmetry. The price we paid is that curvature and torsion must obey some constraints under the action of the interior derivative. These constraints implied on the partial breaking of diffeomorphism invariance. In the present work, we, first, formalize our early results in terms of fiber bundle theory by establishing the formal aspects of the map between a principal bundle (gauge theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism invariance. Then, we study the effect of the constraints on the homology defined by the interior derivative. The result being the emergence of a nontrivial homology in Riemann-Cartan manifolds.

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Section: Nilpotencysupporting

confidence: 84%

“…In this section we discuss the results obtained in [8] in a more formal way. We will focus mainly in the three-dimensional Poincaré case for the CS gauge theory.…”

Section: Nilpotencymentioning

confidence: 99%

Section: Three-dimensional Orthogonal Chern-simons Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological gauge-gravity equivalence: fiber bundle and homology aspects

Assimos¹,

Sobreiro²

2021

Preprint

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Four dimensional topological supergravities from transgression field theory

Concha,

Izaurieta,

Rodríguez

et al. 2024

J. High Energ. Phys.

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In this work, we propose a four-dimensional gauged Wess-Zumino-Witten model, obtained as a dimensional reduction from a transgression field theory invariant under the $$ \mathcal{N} $$ N = 1 Poincaré supergroup. For this purpose, we consider that the two gauge connections on which the transgression action principle depends are given by linear and non-linear realizations of the gauge group respectively. The field content of the resulting four-dimensional theory is given by the gauge fields of the linear connection, in addition to a set of scalar and spinor multiplets in the same representation of the gauge supergroup, which in turn, correspond to the coordinates of the coset space between the gauge group and the five-dimensional Lorentz group. We then decompose the action in terms of four-dimensional quantities and derive the corresponding equations of motion. We extend our analysis to the non- and ultra- relativistic regimes.

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