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Discrete Gauge Anomalies and Instantons
High Energy Physics - Theory · Submitted 15 May 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra.
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We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $\pi_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\pi_3(G)=\mathbb{Z}$, via the fermion zero mode counting. We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. | background 0.65 | 0.67 | 0.04 | asserted 0.66 |
| s1 | The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $\pi_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\pi_3(G)=\mathbb{Z}$, via the fermion zero mode counting. | background 1.00 | 0.06 | 0.05 | asserted 1.00 |
| s2 | We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. | result 0.56 | 0.53 | 0.15 | asserted 1.00 |
| s3 | This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. | gap 0.86 | 0.26 | 0.05 | unclear 0.76 |
| s4 | After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. | result 0.59 | 0.90 | 0.36 | asserted 1.00 |
| s5 | We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$. | result 0.74 | 0.81 | 0.13 | asserted 1.00 |
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Original abstract
We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $\pi_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\pi_3(G)=\mathbb{Z}$, via the fermion zero mode counting. We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$.
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What it cites · 21 sentences without a confident label
Cites as background 5 papers
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The resulting local Calabi-Yau's come with natural quivers that can be inferred from the toric data, which can be used either as the BPS quiver for $d=5$ Seiberg-Witten on a circle when one starts from M-theory on a circle times the Calabi-Yau [ref] , or for constructing (fractional) D3-probe field theories that explore the geometry [ref] .
Dimer models and toric diagrams · Are $SU(N)$ Theories with Anomaly Inflow Safe? · 0.85
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The resulting local Calabi-Yau's come with natural quivers that can be inferred from the toric data, which can be used either as the BPS quiver for $d=5$ Seiberg-Witten on a circle when one starts from M-theory on a circle times the Calabi-Yau [ref] , or for constructing (fractional) D3-probe field theories that explore the geometry [ref] .
Brane Dimers and Quiver Gauge Theories · Are $SU(N)$ Theories with Anomaly Inflow Safe? · 0.85
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The resulting local Calabi-Yau's come with natural quivers that can be inferred from the toric data, which can be used either as the BPS quiver for $d=5$ Seiberg-Witten on a circle when one starts from M-theory on a circle times the Calabi-Yau [ref] , or for constructing (fractional) D3-probe field theories that explore the geometry [ref] .
Brane Tilings and Exceptional Collections · Are $SU(N)$ Theories with Anomaly Inflow Safe? · 0.85
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