Non-Lorentzian Supergravity

Bergshoeff, Eric; Rosseel, Jan

doi:10.1007/978-981-19-3079-9_52-1

Cited by 7 publications

(7 citation statements)

References 61 publications

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“…Instead of verifying whether we have a finite orbit of constraints under supersymmetry, one can alternatively try to solve for the constraints by gauge-fixing and obtain an 11D Membrane Newtonian supergravity multiplet. In the case of 3D supergravity [11,12] this approach has turned out to be very fruitful [11,13]. In that case we found a particle Newton-Cartan supergravity multiplet with the basic fields…”

Section: Gauge-fixingmentioning

confidence: 84%

“…There are divergences of order 𝑐 3 arising from all three terms in the Lagrangian (14). The kinetic term of the three-form even gives rises to two different types of divergences.…”

Section: The Bosonic Casementioning

confidence: 99%

“…Here, 𝜏 𝜇 𝐴 , 𝑒 𝜇 𝑎 and 𝑐 𝜇𝜈𝜌 are the fields that become basic non-relativistic fields after taking the limit 𝑐 → ∞. Substituting the redefinitions ( 16) and (17) into the Lagrangian (14), we obtain the following expansion:…”

Section: The Bosonic Casementioning

confidence: 99%

“…Making the redefinitions ( 16) and ( 17) and using the auxiliary field 𝜆 𝑎𝑏𝑐𝑑 we are now able to take the limit 𝑐 → ∞ of the relativistic action (14). We thus end up with the following non-relativistic action…”

Section: The Bosonic Casementioning

confidence: 99%

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A Consistent Limit of 11D Supergravity

Bergshoeff,

Blair,

Lahnsteiner

et al. 2023

Proceedings of Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2022)

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Motivated by old and new developments in non-relativistic string theory, we show that there exists a consistent non-relativistic limit of eleven-dimensional supergravity. Before taking the limit we give a short review of the underlying Membrane Newton-Cartan geometry. This geometry is a particular extension of the Newton-Cartan geometry in the sense that the two nondegenerate metrics of Newton-Cartan geometry (one to measure time intervals and another one to measure spatial distances) are replaced by two nondegenerate metrics of rank 3 and rank 8, respectively. An important role in describing this geometry and in the consistency of the limit is played by the so-called intrinsic torsion tensor components. These are the components of the torsion tensor that are independent of the spin-connection. After expanding the action of eleven-dimensional supergravity as a power series of a contraction parameter, we show how the different divergences that arise when taking the limit can be tamed. We furthermore show how the divergences that arise in expanding the supersymmetry rules can be controlled by imposing a supersymmetric set of constraints. This leads to a Membrane Newton-Cartan supergravity theory where the Newton potential can be identified with the component of the 3-form of eleven-dimensional supergravity that points in the three directions corresponding to the rank 3 degenerate metric.

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Section: Gauge-fixingmentioning

confidence: 84%

“…There are divergences of order 𝑐 3 arising from all three terms in the Lagrangian (14). The kinetic term of the three-form even gives rises to two different types of divergences.…”

Section: The Bosonic Casementioning

confidence: 99%

Section: The Bosonic Casementioning

confidence: 99%

Section: The Bosonic Casementioning

confidence: 99%

See 2 more Smart Citations

A Consistent Limit of 11D Supergravity

Bergshoeff,

Blair,

Lahnsteiner

et al. 2023

Proceedings of Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2022)

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show abstract

“…Ultra-local models like these are called Carrollian field theories, which have recently gained interest in condensed matter [60,61], fluid dynamics [62][63][64][65], high energy [66][67][68] and gravitational physics [69,70] for diverse inquiries. In particular, fermionic models with these symmetries have been dealt with in detail in [71][72][73]. For ultra-local systems like this, the von Neumann entropy is expected to drop to zero, which is also supported by DMRG calculations.…”

Section: Introductionmentioning

confidence: 80%

Entanglement of edge modes in (very) strongly correlated topological insulators

Ara,

Basu,

Mathew

et al. 2024

J. Phys.: Condens. Matter

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Identifying topological phases for a strongly correlated theory remains a non-trivial task, as defining order parameters, such as Berry phases, is not straightforward. Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition with a suitable definition of order parameters that are related to different entanglement measures for the system. In this work, we study entanglement entropy for a coupled SSH model, both in the presence and absence of Hubbard interaction and at varying interaction strengths. For the free theory, edge entanglement acts as an order parameter, which is supported by analytic calculations and numerical (DMRG) studies. We calculate the symmetry-resolved entanglement and demonstrate the equipartition of entanglement for this model which itself acts as an order parameter when calculated for the edge modes. As the DMRG calculation allows one to go beyond the free theory, we study the entanglement structure of the edge modes in the presence of on-site Hubbard interaction for the same model. A sudden reduction of edge entanglement is obtained as interaction is switched on. The explanation for this lies in the change in the size of the degenerate subspaces in the presence and absence of interaction. We also study the signature of entanglement when the interaction strength becomes extremely strong and demonstrate that the edge entanglement remains protected. In this limit, the energy eigenstates essentially become a tensor product state, implying zero entanglement. However, a remnant entropy survives in the non-trivial topological phase, which is exactly due to the entanglement of the edge modes.

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Extended kinematical 3D gravity theories

Concha,

Pino,

Ravera

et al. 2024

J. High Energ. Phys.

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In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $$ \mathfrak{so} $$ so (2, 2) algebra. We show that the Lie algebra expansion method based on semigroups reproduces not only the original kinematical algebras but also a family of non- and ultra-relativistic algebras. Remarkably, the extended kinematical algebras obtained as sequential expansions of the AdS algebra are characterized by a non-degenerate bilinear invariant form, ensuring the construction of a well-defined Chern-Simons gravity action in three spacetime dimensions. Contrary to the contraction process, the degeneracy of the non-Lorentzian theories is avoided without extending the relativistic algebra but considering a bigger semigroup. Using the properties of the expansion procedure, we show that our construction also applies at the level of the Chern-Simons action.

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Non-Lorentzian Supergravity

Cited by 7 publications

References 61 publications

A Consistent Limit of 11D Supergravity

A Consistent Limit of 11D Supergravity

Entanglement of edge modes in (very) strongly correlated topological insulators

Extended kinematical 3D gravity theories

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