# Anomalies in the space of coupling constants and their dynamical applications II

@article{Crdova2019AnomaliesIT, title={Anomalies in the space of coupling constants and their dynamical applications II}, author={Clay C{\'o}rdova and Daniel S. Freed and Ho Tat Lam and Nathan Seiberg}, journal={arXiv: High Energy Physics - Theory}, year={2019} }

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the $\theta$-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used…

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## References

SHOWING 1-10 OF 151 REFERENCES

Anomalies in the space of coupling constants and their dynamical applications I

- Physics, Mathematics
- 2020

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields…

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

- Physics
- 2017

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum…

Symmetries and Strings in Field Theory and Gravity

- Physics
- 2011

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Zp gauge theories shows…

ANOMALIES AND FERMION ZERO MODES ON STRINGS AND DOMAIN WALLS

- Physics
- 1985

the parity anomaly in 2n + 1 dimensions, and the Dirac index density in 2n + 2 dimensions can be understood in terms of the physics of fermion zero modes on strings and domain walls. We show that the…

Phases Of Adjoint QCD$_3$ And Dualities

- PhysicsSciPost Physics
- 2018

We study 2+1 dimensional gauge theories with a Chern-Simons term and
a fermion in the adjoint representation. We apply general considerations
of symmetries, anomalies, and renormalization group flows…

On 2-group global symmetries and their anomalies

- PhysicsJournal of High Energy Physics
- 2019

A bstractIn general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using…

Generalized global symmetries

- Physics
- 2014

A bstractA q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q…

Supersymmetric Index In Four-Dimensional Gauge Theories

- Physics, Mathematics
- 2000

This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime…

Dynamics of QCD3 with rank-two quarks and duality

- Physics
- 2018

Three-dimensional gauge theories coupled to fermions can develop interesting nonperturbative dynamics. Here we study in detail the dynamics of $SU(N)$ gauge theories coupled to a Dirac fermion in the…

Anomaly constraints on deconfinement and chiral phase transition

- Physics
- 2018

We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless…