Non-Riemannian gravity actions from double field theory

Abstract

Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with nonrelativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

Fractons, geometrically

“…For the Riemannian subspace we have mostly envisaged a Minkowskian signature (4), such that time can flow without suffering from immobility and that the effective mass (33) is not necessarily bigger than the true mass. Alternatively, if we were to choose the Euclidean signature η ab = δ ab and (n, n) = (1, 1) as done in [88] and further in [63,69,70,87,[89][90][91][92], the fracton physics would match that of the non-relativistic string [76][77][78] or torsional/stringy Newton-Cartan gravities [79][80][81][82][83][84][85][86]. Eq.…”

KLT Factorization of Winding String Amplitudes

“…It has also been shown that NCOS is T-dual to nonrelativistic open string theory [27]. Recently, there has been growing interest in nonrelativistic string theory, leading to a plethora of applications to nonrelativistic gravity and field theory (see, e.g., [26,[28][29][30][31][32][33][34][35][36]). Amplitudes for nonrelativistic closed strings have been studied in [23], while amplitudes for nonrelativistic open strings and the associated KLT relation are still in progress [37].…”

Post-Newtonian Feasibility of the Closed String Massless Sector

“…Parametrising the fundamental variables of DFT in terms of the trio {g, B, φ} (c.f. [18][19][20][21][22][23][24][25] for non-Riemannian alternatives), the above single formula is decomposed into…”