mohamed Anber Miami 2018 Based on arxiv180700093 181110642 with Erich Poppitz u of Toronto t Hooft anomalies 2charge Schwinger model and domain walls in hot super YangMills theory Miami 2018 ID: 767067
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mohamed AnberMiami 2018Based on arxiv:1807.00093, 1811.10642 with Erich Poppitz (u of Toronto) 't Hooft anomalies, 2-charge Schwinger model, and domain walls in hot super Yang-Mills theory Miami 2018 M. Anber, Lewis & Clark College 1
OutlineMiami 2018 M. Anber, Lewis & Clark College 2 Overview on domain walls (DW) in hot Super Yang-Mills ‘t Hooft anomaly matching conditions, the new anomalies DW in hot SYM, the worldvolume theory is a Schwinger model ‘t Hooft anomalies in Schwinger model and bulk/DW Physics
OverviewMiami 2018 M. Anber, Lewis & Clark College3 Why we study DW in hot SYM: Prototype of DW in other gauge theories: QCD( adj) for model building Provide a lucid understanding of the new ‘t Hooft anomalies in a weakly coupled setup. Sannino et al Anthenodorou , Bennett, Bergner, Lucini 2014 +many more
OverviewMiami 2018 M. Anber, Lewis & Clark College4 DW in hot SYM (and other YM theories) are the high-T counterparts of center vortices (may play a role in confinement). The physics of hot YM parallels that of YM on a small spatial circle (see Erich Poppitz ’ talk). see, e.g., Greensite book MA, Poppitz , Unsal+many others 2008-now
What is an ‘t Hooft anomalyMiami 2018 M. Anber, Lewis & Clark College 5 ‘t Hooft anomalies: nonperturbative phenomena in QFT, specially the strongly coupled.They put sever constraints on the IR spectrum of asymptotically free theories.‘t Hooft anomalies of symmetries were known since the 80s. ‘t Hooft anomalies of 1-form symmetries non-trivial constraints on the spectrum of a theory. Gaiotto , Kapustin, Komargodski , Seiberg , 2017
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 6 Given a global symmetry of a QFT, we may try to gauge . (turn on a background gauge of )If obstructed (anomalous), the theory has an ‘t Hooft anomaly . ‘t Hooft anomaly is RG invariant, useful for asymptotically free theories. UV IR energy scale ‘t Hooft , 1980
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 7 The UV/IR matching of the anomaly: composite fermions or Goldstone bosons. E.g. 4-D QCD with 2 or 3 fundamental flavors. are global symmetries (act on local operators)
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 8 Gauging : UV IR F quarks fermions GB Frishman , Schwimmer, Banks, Yankielowicz 1981
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 9 Given two symmetries , we can examine one in the background gauge of the other. The obstruction is a mixed ‘t Hooft anomaly. This provides more constraints on the IR spectrum. The lore is that we should check all the ‘t Hooft anomalies of a theory between the UV and IR.
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 10 There are also non-local operators, e.g., line operators (Wilson’s loop) It transforms under global symmetry: C generalized global symmetries Gaiotto , Kapustin, Seiber , Willett, 2014 confined phase
What is an ‘t Hooft anomaly?Miami 2018 M. Anber, Lewis & Clark College 11 It was realized that gauging symmetries provides us with extra ‘t Hooft anomalies.We use the new anomalies to study the physics on the DW in hot super Yang-Mills (SYM). Gaiotto , Kapustin, Komargodski , Seiberg , 2017
SYMMiami 2018 M. Anber, Lewis & Clark College12 4D QCD( adj), including SYM, and symmetries (UV): The breaking can be understood in the BPST instanton background. is a discrete chiral symmetry.
SYMMiami 2018 M. Anber, Lewis & Clark College13 The global symmetries of QCD( adj): We may gauge : (1) couple QCD(adj) to a TQFT (2) turn on twisted ‘t Hooft fluxes on Kapustin, Seiberg 2014 ‘t Hooft 1979, Van Baal 1982
SYMMiami 2018 M. Anber, Lewis & Clark College14 The end result: under we find: Fate of symmetries for SYM at (DW with Chern -Simons theory) mixed ‘t Hooft anomaly
DW in hot SYMMiami 2018 M. Anber, Lewis & Clark College15 Hot SYM: DW Battacharia , Gocksch , Korthals-Altes , Pisarski 1992
DW in SYMMiami 2018 M. Anber, Lewis & Clark College16 The fermions are adjoint+anti-PBC. Recall MA, Poppitz , 2018 Matsubara modes heavy W-bosons
DW in SYMMiami 2018 M. Anber, Lewis & Clark College17 Two fermion zero modes on the DW. DW theory (2-D) is axial Schwinger model: axial with charge 2
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College18 We can relabel the fermions (vector-axial duality in 2-D: ). Thus, -charge vector Schwinger model as EFT on the DW:
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College19 This theory has a non-trivial topology+exactly solvable via bosonization.It enjoys two global symmetries: Under the measure transforms as quantized flux on the 2-torus q=1 by Manton 1985, Iso , Murayama 1990 sum over in path integral
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College20 Thus, only survives. The global symmetries are For these are exactly the global symmetries of the bulk.
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College21 Now, we can gauge by allowing fractional fluxes (‘t Hooft twists):Then, under : Consistent with the bulk/wall anomaly inflow (see Erich Poppitz’s talk) mixed ‘t Hooft anomaly
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College22 The q-charge Schwinger model is exactly solvable: Construct Dirac sea states (gauge fixing, solution of Dirac’s equation in a background gauge) Under : , : The physical states are (cluster decomposition): physical states MA, Poppitz , 2018
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College23 Thus, there are degenerate ground states (they don’t communicate with each other) They satisfy the ‘t Hooft algebraFate of symmetries: is broken: . is broken: string tension vanishes. central extension, sign of anomaly
q-charge Schwinger modelMiami 2018 M. Anber, Lewis & Clark College24 The theory is empty in the IR (no massless excitations) The mixed ‘t Hooft anomaly is matched by a TQFT, as is evident from the anomaly inflow. This picture doesn’t change for QCD(adj ) (adding more adjoint fermions)
ConclusionMiami 2018 M. Anber, Lewis & Clark College25 DW in hot SYM provide the first QFT exactly solvable model to understand the new ‘t Hooft anomalies and the bulk/anomaly inflow. DW worldvolume theory is rich. Center vortices are similar?DW physics calls for lattice confirmation (specially near )