Anomaly of the Electromagnetic Duality of Maxwell Theory

Hsieh, Chang-Tse; Tachikawa, Yuji; Yonekura, Kazuya

doi:10.1103/physrevlett.123.161601

Cited by 48 publications

(101 citation statements)

References 66 publications

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“…3 Another simple example with an anomaly in the space of coupling constants is 4d Maxwell theory viewed as a function of its τ parameter. This follows from the analysis in [8,10], though it was not presented in that language there. 4 Discontinuities in counterterms are a common tool for deducing phase transitions.…”

Section: Anomalies In Yang-mills Theorymentioning

confidence: 99%

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

et al. 2020

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We extend our earlier work on anomalies in the space of coupling constants to fourdimensional 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 θ-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 to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study SUpNq and SppNq gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the θ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

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Section: Anomalies In Yang-mills Theorymentioning

confidence: 99%

“…bundle with second SW class B L and B R by tensoring n P SUp2q bundles with second SW class B L and n P SUp2q bundles10 The instanton number of a Spinp4n`2q{Z 4 bundle with second SW class B is ş H 4 pX, Z 4 q, so for N " 4n`2 " 2 mod 8 the instanton number is ş PpBq while for N " 4n`2 " 6 mod 8 the instanton number is´ş 1 4…”

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confidence: 99%

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

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“…Let us sketch how the computation using the equivariant index theorem goes. 6 Suppose X =X/G andX = ∂W where G acts onW such that the fixed points of the action of G are isolated points on the interior of W , see Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of the Op − -planes, the U(1) gauge fields on Dq-branes also contribute to the anomaly. See[6] for the case of the O3 − -plane.…”

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confidence: 99%

Why are fractional charges of orientifolds compatible with Dirac quantization?

2019

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Orientifold p-planes with p ≤ 4 have fractional Dp-charges, and therefore appear inconsistent with Dirac quantization with respect to D(6−p)-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the η invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases.In an appendix, we point out that the duality group of type IIB string theory is the pin + version of the double cover of GL(2, Z).

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“…+ m 1 q, e 2 p + m 2 q) = exp 2πi N (e 1 m 2 − e 2 m 1 ) (3.23) from (3.5), where p and q denote the A and B cycles of the torus, respectively. Here e i and m i denote the Wilson and 't Hooft charges of the associated line operators, respectively.24 See[59][60][61][62] for recent work studying other aspects of anomalies on the space of coupling constants.…”

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confidence: 99%

IIB flux non-commutativity and the global structure of field theories

García-Etxebarria

Heidenreich

Regalado

2019

J. High Energ. Phys.

181

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We discuss the origin of the choice of global structure for six dimensional (2, 0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of N = 4 theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of N = 4 ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional (1, 0) theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects. arXiv:1908.08027v2 [hep-th] 9 Oct 20191 The separation into background and intrinsic data is sometimes arbitrary: if we restrict ourselves to fourdimensional Yang-Mills theories with constant coupling τ we could view τ as part of the data defining T . However, if we wish to allow for the possibility that τ varies across M then we must include it as part of the background data to be specified for each manifold. The second interpretation will be more natural from the point of view in this paper, and such configurations will play an interesting role below.2 In this paper we will take M6 to be closed, Spin and orientable, and furthermore we will assume that the cohomology groups of M6 are freely generated, so there is no torsion. 3 The free, or "abelian", (2, 0) theory can be obtained by replacing C 2 /Γ by a single-centered Taub-NUT space.5 The two groups are related by the short exact sequence 0 → W 4 → H 4 (M6 × S 3 /Zn; U (1)) → Tor(H 5 (M6 × S 3 /ZN ; Z)) → 0 , with W 4 the group of topologically trivial C4 Wilson lines on M6 × S 3 /Zn.

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Anomaly of the Electromagnetic Duality of Maxwell Theory

Cited by 48 publications

References 66 publications

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

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

Why are fractional charges of orientifolds compatible with Dirac quantization?

IIB flux non-commutativity and the global structure of field theories

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