12 research outputs found
Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
We present non- and ultra-relativistic Jackiw-Teitelboim (JT) supergravity as
metric BF theories based on the extended Newton-Hooke and extended AdS Carroll
superalgebras in two spacetime dimensions, respectively. The extended
Newton-Hooke structure, and, in particular, the invariant metric necessary for
the BF construction of non-relativistic JT supergravity, is obtained by
performing an expansion of the AdS superalgebra.
Subsequently, we introduce the extended AdS Carroll superalgebra, and the
associated invariant metric, as a suitable redefinition of the extended
Newton-Hooke superalgebra. The mapping involved can be seen as the
supersymmetric extension of the duality existing at the purely bosonic level
between the extended Newton-Hooke algebra with (positive) negative cosmological
constant and the extended (A)dS Carroll algebra in two dimensions. Finally, we
provide the Carrollian JT supergravity action in the BF formalism. Moreover, we
show that both the non-relativistic and the ultra-relativistic theories
presented can also be obtained by direct expansion of JT
supergravity.Comment: 25 page
Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions
We provide a Lie algebra expansion procedure to construct three-dimensional
higher-order Schr\"odinger algebras which relies on a particular subalgebra of
the four-dimensional relativistic conformal algebra. In particular, we
reproduce the extended Schr\"odinger algebra and provide a new higher-order
Schr\"odinger algebra. The structure of this new algebra leads to a discussion
on the uniqueness of the higher-order non-relativistic algebras. Especially, we
show that the recent d-dimensional symmetry algebra of an action principle for
Newtonian gravity is not uniquely defined but can accommodate three discrete
parameters. For a particular choice of these parameters, the Bargmann algebra
becomes a subalgebra of that extended algebra which allows one to introduce a
mass current in a Bargmann-invariant sense to the extended theory.Comment: v3., typos fixed, reference added, version appeared in JHE
Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
We derive the action and symmetries of the bosonic sector of non-Lorentzian
IIB supergravity by taking the non-relativistic string limit. We find that the
bosonic field content is extended by a Lagrange multiplier that implements a
restriction on the Ramond-Ramond fluxes. We show that the SL(2,R)
transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear
polynomial realization. Using classical invariant theory of polynomial
equations and binary forms, we will develop a general formalism describing the
polynomial realization of SL(2,R) and apply it to the special case of
non-Lorentzian IIB supergravity. Using the same formalism, we classify all the
relevant SL(2,R) invariants. Invoking other bosonic symmetries, such as the
local boost and dilatation symmetry, we show how the bosonic part of the
non-Lorentzian IIB supergravity action is formed uniquely from these SL(2,R)
invariants. This work also points towards the concept of a non-Lorentzian
bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to
bootstrap the bosonic dynamics in Lorentzian supergravity, without considering
the fermions.Comment: 43 page
Branched SL(2,ℤ) duality
We investigate how SL(2,ℤ) duality is realized in nonrelativistic type IIB superstring theory, which is a self-contained corner of relativistic string theory. Within this corner, we realize manifestly SL(2,ℤ)-invariant (p, q)-string actions. The construction of these actions imposes a branching between strings of opposite charges associated with the two-form fields. The branch point is determined by these charges and the axion background field. Both branches must be incorporated in order to realize the full SL(2,ℤ) group. Besides these string actions, we also construct D-instanton and D3-brane actions that manifestly realize the branched SL(2,ℤ) symmetry
Non-Lorentzian IIB supergravity from a polynomial realization of SL(2, â„ť)
Abstract We derive the action and symmetries of the bosonic sector of non-Lorentzian IIB supergravity by taking the non-relativistic string limit. We find that the bosonic field content is extended by a Lagrange multiplier that implements a restriction on the Ramond-Ramond fluxes. We show that the SL(2, â„ť) transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear polynomial realization. Using classical invariant theory of polynomial equations and binary forms, we will develop a general formalism describing the polynomial realization of SL(2, â„ť) and apply it to the special case of non-Lorentzian IIB supergravity. Using the same formalism, we classify all the relevant SL(2, â„ť) invariants. Invoking other bosonic symmetries, such as the local boost and dilatation symmetry, we show how the bosonic part of the non-Lorentzian IIB supergravity action is formed uniquely from these SL(2, â„ť) invariants. This work also points towards the concept of a non-Lorentzian bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to bootstrap the bosonic dynamics in Lorentzian supergravity, without considering the fermions