Modified instanton sum in QCD and higher-groups

Abstract

We consider the SU (N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2πperiodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only Z N 1-form symmetry but also Z p 3-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching. The computation of 't Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-N and also the reliable semiclassics on R 3 × S 1 , and we find that the topological susceptibility plays a role of the order parameter for the Z p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by Z p , and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the 't Hooft anomaly.

Deconfinement on axion domain walls

“…We show that the deconfinement and rearrangement of heavy degrees of freedom on the axion domain wall are intertwined. We use a calculable compactification [21,22] to R 3 × S 1 to study the mechanism of deconfinement, following the observations of our work with Sulejmanpasic [23] and the recent remarks on anomaly matching [24]. Here, the physics of confinement is semiclassical and the failure of the axion EFT can be traced to the multi-branch nature of its potential (which, in this setup, is seen at any finite N c ).…”

“…2 (∂ µ a) 2 . To further discuss the long-distance dynamics, we now borrow the results of the recent study of deformed Yang-Mills theory with θ parameter [24], adding the dynamical axion field and its topological coupling to the background fields from (2.8).…”

“…14 See [37] for an earlier study of axions coupled to deformed Yang-Mills theory. 15 The careful reader might notice a slight difference in (3.1) from the formulae of [24] stemming from the different form of the fundamental S 1 Wilson loop we use; no aspects of the physics are changed. 16 For brevity and to reduce clutter, we do not explicitly indicate the three dimensional nature of all forms that appear below.…”

Deconfinement and CP breaking at θ=π in Yang-Mills theories and a novel phase for SU(2)

“…That is, the quantum phase transitions of softly broken SYM on small R 3 × S 1 are smoothly connected to the thermal phase transitions of pure YM theory. This is the adiabatic continuity conjecture, and a lot of circumstantial evidences have been obtained so far [58][59][60][61][62][63][64][65][66][67][68][69][82][83][84][85][86][87][88][89][90]], although we do not have a direct proof yet.…”

Universality between vector-like and chiral quiver gauge theories: anomalies and domain walls

“…Moreover, we expect that the adiabatic continuity works, which is a milder version of volume independence, and the dynamics obtained in the above semiclassics shows qualitatively the same behavior of the strongly-coupled dynamics on R 4 . Even though this is a very nontrivial conjecture, it provides a very useful information on dynamics, and it turns out that the constraint by anomaly is indeed satisfied [48] (For related previous studies, see, e.g., refs. [26][27][28]).…”