Anomalies of 4d $Spin_G$ Theories
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| author | Brennan, T. Daniel Intriligator, Kenneth |
| author_facet | Brennan, T. Daniel Intriligator, Kenneth |
| contents | We consider 't Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits $Spin_G(4)$ generalized spin structure, with $G$ either gauged or a global symmetry. We discuss methods to directly compute $w_2\cup w_3$ 't Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g. $M_4=\mathbb{CP}^2$. Such anomalies have been discussed for $SU(2)$ gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of ${\cal N}=2$ SYM theory. We directly compute these anomalies for a variety of theories, including general $G$ gauge theories with adjoint fermions, $SU(2)$ gauge theory with fermions in general representations, and $Spin(N)$ gauge theories with fundamental matter. We discuss aspects of matching these and other 't Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for general $G_{\rm gauge}$ theory with $N_f$ adjoint Weyl fermions. For example, in the case of $N_f=2$ we discuss anomaly matching in the IR phase consisting of $h^\vee _{G_{\rm gauge}}$ copies of a $\mathbb{CP}^1$ non-linear sigma model, including for the $w_2w_3$ anomalies when formulated with $Spin_{SU(2)_{\rm global}}(4)$ structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04756 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anomalies of 4d $Spin_G$ Theories Brennan, T. Daniel Intriligator, Kenneth High Energy Physics - Theory We consider 't Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits $Spin_G(4)$ generalized spin structure, with $G$ either gauged or a global symmetry. We discuss methods to directly compute $w_2\cup w_3$ 't Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g. $M_4=\mathbb{CP}^2$. Such anomalies have been discussed for $SU(2)$ gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of ${\cal N}=2$ SYM theory. We directly compute these anomalies for a variety of theories, including general $G$ gauge theories with adjoint fermions, $SU(2)$ gauge theory with fermions in general representations, and $Spin(N)$ gauge theories with fundamental matter. We discuss aspects of matching these and other 't Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for general $G_{\rm gauge}$ theory with $N_f$ adjoint Weyl fermions. For example, in the case of $N_f=2$ we discuss anomaly matching in the IR phase consisting of $h^\vee _{G_{\rm gauge}}$ copies of a $\mathbb{CP}^1$ non-linear sigma model, including for the $w_2w_3$ anomalies when formulated with $Spin_{SU(2)_{\rm global}}(4)$ structure. |
| title | Anomalies of 4d $Spin_G$ Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.04756 |