Bootstrapping MN and tetragonal CFTs in three dimensions

Abstract

Conformal field theories (CFTs) with MN and tetragonal global symmetry in d = 2 + 1 dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. In the tetragonal case, no new kinks are found. Estimates for critical exponents are provided for a few cases describing phase transitions in various materials. In two particular MN cases, corresponding to theories with global symmetry groups O(2) 2 S 2 and O(2) 3 S 3 , a second kink is found. In the O(2) 2 S 2 case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO 2 and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2) 3 S 3 case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

“…As expected, for smaller values of n the agreement between large-n and numerical predictions becomes progressively worse. For n = 2 we find a pronounced kink that appears to correspond to a known fixed point of the expansion as discussed in [39]. In the n = 3 case, there exist mild kinks that we study extensively with a mixed correlator system.…”

“…As discussed in Appendix C, the single-correlator crossing equations of the O 2,2 = O(2) 2 / 2 theory are equivalent to those of the MN 2,2 = O(2) 2 S 2 theory discussed in [39]. A strong kink was obtained in the X sector of [39] (see Fig. 1 there), which corresponds to the Z sector in (93) below.…”

“…14 does not correspond to the O 2,2 chiral fixed point. In [39] it was suggested that this kink may correspond to the fully-interacting theory of the expansion analyzed in [71][72][73][74]. To continue our search for the O 2,2 chiral fixed point, we obtain a bound on the dimension of the first scalar operator in the WX representation.…”

“…In the O 2,2 case, the collinear fixed point is equivalent to the O(2) fixed point [51], and so we will only be examining the proposed chiral fixed point [51,54]. As discussed in Appendix C, the single-correlator crossing equations of the O 2,2 = O(2) 2 / 2 theory are equivalent to those of the MN 2,2 = O(2) 2 S 2 theory discussed in [39]. A strong kink was obtained in the X sector of [39] (see Fig.…”

Bootstrapping mixed correlators in three-dimensional cubic theories

“…It has been observed in practice that the bootstrap of subgroups of O(N ), for some value of N , always present scalar singlet sector bounds identical to O(N ) ones. Known examples include hypercubic and hypertetrahedral theories[10], MN and tetragonal theories[22] and O(m) × O(n) theories[23].…”