Local Anomaly Cancellation and Equivariant Cohomology of Jet Bundles

2016 ◽  
pp. 101-106
Author(s):  
Roberto Ferreiro Pérez
Keyword(s):  
Equivariant Cohomology ◽  
Anomaly Cancellation ◽  
Jet Bundles ◽  
Local Anomaly

scholarly journals An M-Theory Perspective on Heterotic K3 Orbifold Compactifications

2003 ◽  
Vol 18 (19) ◽  
pp. 3273-3314 ◽  
Author(s):  
Michael Faux ◽  
Dieter Lüst ◽  
Burt A. Ovrut
Keyword(s):  
Twisted Sector ◽  
Anomaly Cancellation ◽  
Local Anomaly ◽  
Dimensional Models ◽  
M Theory

We analyze the structure of heterotic M-theory on K3 orbifolds by presenting a comprehensive sequence of M-theoretic models constructed on the basis of local anomaly cancellation. This is facilitated by extending the technology developed in our previous papers to allow one to determine "twisted" sector states in nonprime orbifolds. These methods should naturally generalize to four-dimensional models, which are of potential phenomenological interest.

scholarly journals Intersecting orbifold planes and local anomaly cancellation in M-theory

1999 ◽  
Vol 554 (1-2) ◽  
pp. 437-483 ◽  
Author(s):  
Michael Faux ◽  
Dieter Lüst ◽  
Burt A. Ovrut
Keyword(s):  
Anomaly Cancellation ◽  
Local Anomaly ◽  
M Theory

scholarly journals GAUGED WZW MODELS VIA EQUIVARIANT COHOMOLOGY

2011 ◽  
Vol 26 (18) ◽  
pp. 1343-1352
Author(s):  
HUGO GARCÍA-COMPEÁN ◽  
PABLO PANIAGUA
Keyword(s):  
Equivariant Cohomology ◽  
Higher Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Anomaly Cancellation ◽  
Gauge Invariant ◽  
Cancellation Condition ◽  
Four Dimensions ◽  
Invariant Extension

The problem of finding a systematic computation of the gauge-invariant extension of WZW term by using equivariant cohomology is addressed. Witten's analysis for the two-dimensional case is extended to higher dimensions, in particular to four dimensions. It is shown that Cartan's model is used to find the anomaly cancellation condition while Weil's model is more appropriated to express the gauge-invariant extension of the WZW term. In the process we point out that both models are also useful to emphasize some nice relations with the Abelian anomaly.

scholarly journals Local anomaly cancellation, M-theory orbifolds and phase-transitions

2000 ◽  
Vol 589 (1-2) ◽  
pp. 269-291 ◽  
Author(s):  
Michael Faux ◽  
Dieter Lüst ◽  
Burt A. Ovrut
Keyword(s):  
Phase Transitions ◽  
Anomaly Cancellation ◽  
Local Anomaly ◽  
M Theory

scholarly journals Twisted Sectors and Chern–Simons Terms in M-Theory Orbifolds

2003 ◽  
Vol 18 (17) ◽  
pp. 2995-3013 ◽  
Author(s):  
Michael Faux ◽  
Dieter Lüst ◽  
Burt A. Ovrut
Keyword(s):  
Twisted Sector ◽  
Anomaly Cancellation ◽  
Local Anomaly ◽  
M Theory ◽  
Chern Simons ◽  
Gravitational Anomalies

It is shown that the twisted sector spectrum, as well as the associated Chern–Simons interactions, can be determined on M-theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes arising within the context of an explicit R6 × S1/Z2 × T4/Z2 orbifold, although the results are completely general. Local anomaly cancellation in this context is shown to require fractional anomaly data that can only arise from a twisted sector on the seven-planes, thus determining the twisted spectrum up to a small ambiguity. These results open the door to the construction of arbitrary M-theory orbifolds, including those containing fixed four-planes which are of phenomenological interest.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals A note on gauge anomaly cancellation in effective field theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ferruccio Feruglio
Keyword(s):  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Anomaly Cancellation ◽  
Charge Assignment ◽  
The Standard Model ◽  
Renormalizable Theory ◽  
Complete Set ◽  
Gauge Anomalies ◽  
Gauge Anomaly

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

scholarly journals Omega vs. pi, and 6d anomaly cancellation

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joe Davighi ◽  
Nakarin Lohitsiri
Keyword(s):  
Gauge Theories ◽  
Necessary Conditions ◽  
Homotopy Groups ◽  
Mapping Torus ◽  
Anomaly Cancellation ◽  
Global Anomaly ◽  
Gauge Anomalies ◽  
Local Anomalies ◽  
Dimensional Mapping

Abstract In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.

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