Galilean Kalb-Ramond Field
Abstract
We construct Galilean limits of the free Kalb--Ramond two-form gauge field and analyze their symmetries using two different procedures. An Inönü--Wigner contraction of the D-dimensional equations of motion results in two inequivalent electric and magnetic limits. In both cases the equations are invariant under the complete infinite-dimensional Galilean conformal algebra (GCA) only at D=6, the critical dimension of the relativistic theory. The second procedure is a null reduction of the (D+1)-dimensional theory which yields a local action for a four-field multiplet. In the zero-momentum sector, the resulting action is invariant under translations, rotations, Galilean boosts and an anisotropic dilatation with dynamical exponent z. However, in contrast to Galilean electrodynamics, it is not invariant under the special conformal generators of the GCA (and its higher modes). We attribute this to the vector residing at the bottom of the boost chain. If the parent theory is taken to be the six-dimensional conformal one, the resulting five-dimensional reduced action is invariant under the Schrödinger special conformal transformation with z=2 which is derived from the relativistic conformal group. In light-cone gauge, the non-zero null momentum sectors reduce to free Schrödinger fields. We obtain the gauge-fixed propagator, which is instantaneous, and compare the free-field correlators with the two-point functions allowed by the Ward identities of both.
Related
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BibTeX
@misc{mehra2026galilean,
title = {{Galilean Kalb-Ramond Field}},
author = {Aditya Mehra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01097},
eprint = {2609.01097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01097},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Galilean Kalb-Ramond Field
AU - Aditya Mehra
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01097
UR - https://arxiv.org/abs/2609.01097
AB - We construct Galilean limits of the free Kalb--Ramond two-form gauge field and analyze their symmetries using two different procedures. An Inönü--Wigner contraction of the D-dimensional equations of motion results in two inequivalent electric and magnetic limits. In both cases the equations are invariant under the complete infinite-dimensional Galilean conformal algebra (GCA) only at D=6, the critical dimension of the relativistic theory. The second procedure is a null reduction of the (D+1)-dimensional theory which yields a local action for a four-field multiplet. In the zero-momentum sector, the resulting action is invariant under translations, rotations, Galilean boosts and an anisotropic dilatation with dynamical exponent z. However, in contrast to Galilean electrodynamics, it is not invariant under the special conformal generators of the GCA (and its higher modes). We attribute this to the vector residing at the bottom of the boost chain. If the parent theory is taken to be the six-dimensional conformal one, the resulting five-dimensional reduced action is invariant under the Schrödinger special conformal transformation with z=2 which is derived from the relativistic conformal group. In light-cone gauge, the non-zero null momentum sectors reduce to free Schrödinger fields. We obtain the gauge-fixed propagator, which is instantaneous, and compare the free-field correlators with the two-point functions allowed by the Ward identities of both.
ER -