Uniqueness of Galilean conformal electrodynamics and its dynamical structure

Self Cite

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges.

Section: Discussionmentioning

confidence: 99%

Section: Helmholtz Conditions For Carrollian Scalar Edmentioning

confidence: 99%

See 1 more Smart Citation

Field theories on null manifolds

Bagchi

Basu

Mehra

et al. 2020

Self Cite

“…The theory (2.11) does not possess propagating degrees of freedom. This can be seen by exploring the structure of the poles in the gauge field propagator, or alternatively by a Dirac constraint analysis, see, e.g., [47]. 12 To introduce some propagating degrees of freedom, we couple the GED theory to a Schrödinger scalar field σ.…”

Section: Jhep10(2020)195mentioning

confidence: 99%

Renormalization of Galilean electrodynamics

Chapman

Pietro

Yan

2020

We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrödinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic Maxwell theory coupled to a complex scalar field in 3+1 dimensions and is closely related to the Galilean electromagnetism of Le-Bellac and Lévy-Leblond. Due to the presence of a dimensionless, gauge-invariant scalar field in the Galilean multiplet of the gauge-field, we find that at the quantum level an infinite number of couplings is generated. We explain how to handle the quantum corrections systematically using the background field method. Due to a non-renormalization theorem, the beta function of the gauge coupling is found to vanish to all orders in perturbation theory, leading to a continuous family of fixed points where the non-relativistic conformal symmetry is preserved.

“…At leading order in α and in the flat closed string background, the DBI action in (4.6) gives rise to Galilean Electrodynamics (GED). GED is a non-dynamical U(1) gauge theory that is invariant under a Galilean boost transformation, and has been studied at the classical level in [18][19][20]36]. In [37], the one-loop beta-functions of Galilean electrodynamics coupled to a Schrödinger scalar in 2 + 1 dimensions are computed, where the renormalization of the dynamical Schrödinger scalar receives highly nontrivial contributions from interactions with the non-dynamical gauge sector.…”

Section: Galilean Electrodynamics On a Newton-cartan Backgroundmentioning

confidence: 99%

Nonrelativistic open string and Yang-Mills theory

Gomis

Yan

2021

The classical and quantum worldsheet theory describing nonrelativistic open string theory in an arbitrary nonrelativistic open and closed string background is constructed. We show that the low energy dynamics of open strings ending on n coincident D-branes in flat spacetime is described by a Galilean invariant U(n) Yang-Mills theory. We also study nonrelativistic open string excitations with winding number and demonstrate that their dynamics can be encoded into a local gauge theory in one higher dimension. By demanding conformal invariance of the boundary couplings, the nonlinear equations of motion that govern the consistent open string backgrounds coupled to an arbitrary closed background (described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field) are derived and shown to emerge from a Galilean invariant Dirac-Born-Infeld type action.