RG limit cycles and unconventional fixed points in perturbative QFT

In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in D = 4 space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large N gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in [1, 2] where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions.In our case, the theories demonstrating the above features have gauge groups which are specific products of SO(N) in one family and SU(N) in the other. Working in a perturbative regime at the N → ∞ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is ℤ2 in one family of theories and U(1) in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.

Section: F32 Diagrams Corresponding To Vertex Renormalizations Of Double Trace Couplingsmentioning

confidence: 56%

Section: Planar Equivalence Between the Two Double Bifundamental Modelsmentioning

confidence: 99%

Section: F32 Diagrams Corresponding To Vertex Renormalizations Of Double Trace Couplingsmentioning

confidence: 99%

See 1 more Smart Citation

Thermal order in large N conformal gauge theories

Chaudhuri

Choi

Rabinovici

2021

“…(in the second case the CFT is however non-unitary), while the latter can have complex scaling dimensions without their complex conjugate partner. Examples of real non-unitary CFTs are provided by the Wilson-Fisher fixed point in non-integer dimension [93] or by the symmetric traceless O(N ) model [94], while an example of complex CFT, with dimensions not on the principal series, is offered by the Q-state Potts model with Q > 4 [95]. In this respect, we notice that a simple corollary of Proposition 1 is the following:…”

Section: Jhep05(2021)004mentioning

confidence: 94%

Instability of complex CFTs with operators in the principal series

Benedetti

2021

We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

“…7 We will continue to work in this limit. In this limit, there is an orbifold equivalence [36][37][38][39][40][41][42][43][44][45] between the RDB model and the CDB model [1] with the couplings in the two dual theories related by…”

Section: Jhep08(2021)148mentioning

confidence: 99%

Symmetry breaking at high temperatures in large N gauge theories

Chaudhuri

Rabinovici

2021

Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.