Vierbein interactions with antisymmetric components

Abstract

In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields. The theory is the fully diffeomorphism and local Lorentz invariant extension of a previous construction which involved a fixed reference vierbein. Certain vierbein components can be shifted by local Lorentz transformations and do not enter the associated metric tensors. We parameterize these components by an antisymmetric tensor field and give them a kinetic term in the action, thereby promoting them to dynamical variables. In addition, the action contains two Einstein-Hilbert terms and an interaction potential whose form is inspired by ghost-free massive gravity and bimetric theory. The resulting theory describes the interactions of a massless spin-2, a massive spin-2 and an antisymmetric tensor field. It can be generalized to the case of multiple massive spin-2 fields and multiple antisymmetric tensor fields. The absence of additional and potentially pathological degrees of freedom is verified in an ADM analysis. However, the antisymmetric tensor fluctuation around the maximally symmetric background solution has a tachyonic mass pole.

On the duality of massive Kalb-Ramond and Proca fields

“…Despite this, a number of claims of duality between the two theories have recently appeared in the literature (see eg. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In other words, both theories are said to describe the same physical system [22].…”

“…This indicates a contradiction with the numerous claims in the literature (see eg. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]) that these theories are dual to each other.…”

On the duality of massive Kalb-Ramond and Proca fields

“…Despite this, a number of claims of duality between the two theories have recently appeared in the literature (see eg. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In other words, both theories are said to describe the same physical system [22].…”

“…This contradicts the numerous claims in the literature (see eg. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]) that these theories are dual to each other, which is shown to be false. We show that the difference between the theories can be traced already to the free theories without a self-interaction by studying the behavior of quantum fluctuations for different modes.…”