Two-flavor adjoint QCD

Abstract

We study four dimensional SU (2) Yang-Mills theory with two massless adjoint Weyl fermions. When compactified on a spatial circle of size L much smaller than the strong-coupling scale, this theory can be solved by weak-coupling nonperturbative semiclassical methods. We study the possible realizations of symmetries in the R 4 limit and find that all continuous and discrete 0-form and 1form 't Hooft anomaly matching conditions are saturated by a symmetry realization and massless spectrum identical to that found in the small-L limit, with only a single massless flavor-doublet fermion in the infrared. This observation raises the possibility that the class of theories which undergo no phase transition between the analytically-solvable small-size circle and strongly-coupled infinite-size circle is larger than previously thought, and offers new challenges for lattice studies.

Generalized ’t Hooft anomalies on non-spin manifolds

“…In particular, as (3.14, 3.15) show, there is a mixed anomaly between the discrete chiral and center symmetries (the 't Hooft fluxes m, m , m c ) which cannot be matched by the IR fermions. This was already recognized in [30], where it was proposed that there is spontaneous breaking of the chiral symmetry, Z 8 → Z 4 , by a four-fermion condensate detλ i λ j 15 13 The U (1)B background is taken to have an extra flux m B ∈ Z,…”

“…The usual lore is that these theories will either flow to an IR conformal field theory or break their global symmetries, including the discrete chiral symmetry Z 4NcN f . However, more exotic scenarios have recently been discussed in [23,28,[30][31][32]. 12 In [30], we conjectured that the theory with N c = 2 and a single N f = 1 Dirac fermion will form a massless composite, schematically given by (λ) 3 , a doublet under the enhanced SU (2N f ) = SU (2) flavor symmetry, accompanied by the breaking Z 8 → Z 4 , due to an SU (2) invariant four-fermion condensate.…”

“…However, more exotic scenarios have recently been discussed in [23,28,[30][31][32]. 12 In [30], we conjectured that the theory with N c = 2 and a single N f = 1 Dirac fermion will form a massless composite, schematically given by (λ) 3 , a doublet under the enhanced SU (2N f ) = SU (2) flavor symmetry, accompanied by the breaking Z 8 → Z 4 , due to an SU (2) invariant four-fermion condensate. This IR scenario has to be supplemented by a TQFT that matches a mixed anomaly between the 0-form discrete chiral and 1-form center symmetries on non-spin backgrounds [23], further studied in [16,19,31].…”

“…Thus, Z U V transforms by a Z 2NcN f phase for general values of the background BCF fluxes. Now, we first examine the IR scenario [30] for N c = 2 and a single Dirac fermion N f = 1. The IR composite Dirac fermion has unit charge under U (1) B and charge 3 under the Z 8 discrete chiral symmetry.…”

“…In Section 3.1.1 we discuss QCD(adj). Our intention is to use the present study to investigate the various scenarios for IR behavior, whose consistency has been recently elaborated upon in [16,19,23,28,[30][31][32]. In Section 3.1.2, we study an SU (6) gauge theory with a single Dirac flavor in the two-index antisymmetric representation and, in Section 3.1.3, its generalization to SU (4k+2) with a single flavor of twoindex symmetric or antisymmetric representations.…”