Critical Field Theories with OSp(1|2M) Symmetry

In the paper [L. Fei et al., J. High Energy Phys. 09 (2015) 076] a cubic field theory of a scalar field sigma and two anticommuting scalar fields, theta and (theta) over bar, was formulated. In 6 - epsilon dimensions it has a weakly coupled fixed point with imaginary cubic couplings where the symmetry is enhanced to the supergroup OSp(1 vertical bar 2)). This theory may be viewed as a UV completion in 2 < d < 6 of the nonlinear sigma model with hyperbolic target space H-0 vertical bar 2 described by a pair of intrinsic anticommuting coordinates. It also describes the q -> 0 limit of the critical q-state Potts model, which is equivalent to the statistical mechanics of spanning forests on a graph. In this Letter we generalize these results to a class of OSp vertical bar 2M symmetric field theories whose upper critical dimensions are d(c)(M) = 2[2M+1)/(2M - 1)]. They contain 2M anticommuting scalar fields, theta(i), (theta) over bar (i) and one commuting one, with interaction g(sigma(2) + 2 theta(i)(theta) over bar (i(2M+1)/2). In d(c)(M)-epsilon dimensions, we find a weakly coupled IR fixed point at an imaginary value of g. We propose that these critical theories are the UV completions of the sigma models with fermionic hyperbolic target spaces H-0 vertical bar 2M. Of particular interest is the quintic field theory with OSp(1 vertical bar 4)) symmetry, whose upper critical dimension is 10/3. Using this theory, we make a prediction for the critical behavior of the OSp(1 vertical bar 4) lattice system in three dimensions.

Automated summary

In this paper, a cubic field theory involving scalar and anticommuting scalar fields is formulated. The results are generalized to a class of symmetric field theories with specific critical dimensions. The critical theories are proposed to be the UV completions of sigma models with specific properties. The quintic field theory with OSp(1 vertical bar 4)) symmetry is of particular interest and is used to predict the critical behavior of a lattice system.