Anomaly cancellation in seven-dimensional supergravity with a boundary

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.

Download Full-text

Omega vs. pi, and 6d anomaly cancellation

Journal of High Energy Physics ◽

10.1007/jhep05(2021)267 ◽

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.

Download Full-text

Transgression and twisted anomaly cancellation formulas on odd dimensional manifolds

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2009.12.006 ◽

2010 ◽

Vol 60 (4) ◽

pp. 611-622 ◽

Cited By ~ 2

Author(s):

Yong Wang

Keyword(s):

Anomaly Cancellation ◽

Cancellation Formulas

Download Full-text

Anomaly cancellation in six dimensions

Journal of Mathematical Physics ◽

10.1063/1.530885 ◽

1994 ◽

Vol 35 (4) ◽

pp. 1819-1833 ◽

Cited By ~ 120

Author(s):

Jens Erler

Keyword(s):

Anomaly Cancellation ◽

Six Dimensions

Download Full-text

The supersymmetric version of the Green-Schwarz anomaly cancellation mechanism

Physics Letters B ◽

10.1016/0370-2693(94)90860-5 ◽

1994 ◽

Vol 332 (1-2) ◽

pp. 71-76 ◽

Cited By ~ 4

Author(s):

Antonio Candiello ◽

Kurt Lechner

Keyword(s):

Anomaly Cancellation ◽

Supersymmetric Version

Download Full-text

Universality, exponents and anomaly cancellation in disordered Dirac fermions

Nuclear Physics B ◽

10.1016/j.nuclphysb.2013.07.007 ◽

2013 ◽

Vol 875 (2) ◽

pp. 408-422 ◽

Cited By ~ 1

Author(s):

Vieri Mastropietro

Keyword(s):

Dirac Fermions ◽

Anomaly Cancellation

Download Full-text

Some comments on 6d global gauge anomalies

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptab015 ◽

2021 ◽

Author(s):

Yasunori Lee ◽

Yuji Tachikawa

Keyword(s):

Point Of View ◽

Homotopy Groups ◽

Proper Treatment ◽

Anomaly Cancellation ◽

The Past ◽

Global Gauge ◽

Gauge Anomalies

Abstract Global gauge anomalies in 6d associated with non-trivial homotopy groups π6(G) for G = SU(2), SU(3), and G2 were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups Ω7spin (BG), which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the 6d Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from π6(G). In this paper, we revisit and clarify the relation between these two different approaches.

Download Full-text

Supersymmetry Breaking in a Minimal Anomalous Extension of the MSSM

ISRN High Energy Physics ◽

10.5402/2012/903106 ◽

2012 ◽

Vol 2012 ◽

pp. 1-31 ◽

Cited By ~ 1

Author(s):

A. Lionetto ◽

A. Racioppi

Keyword(s):

Supersymmetry Breaking ◽

Effective Action ◽

Anomaly Cancellation ◽

Gauge Symmetries ◽

Breaking Mechanism ◽

Soft Supersymmetry Breaking ◽

Brane Models

We study a supersymmetry breaking mechanism in the context of a minimal anomalous extension of the MSSM. The anomaly cancellation mechanism is achieved through suitable counterterms in the effective action, that is, the Green-Schwarz terms. We assume that the standard MSSM superpotential is perturbatively realized; that is, all terms allowed by gauge symmetries except for the μ-term which has a nonperturbative origin. The presence of this term is expected in many intersecting D-brane models which can be considered as the ultraviolet completion of our model. We show how soft supersymmetry breaking terms arise in this framework, and we study the effect of some phenomenological constraints on this scenario.

Download Full-text

Fermion mass hierarchies from supersymmetric gauged flavour symmetry in 5D

SciPost Physics ◽

10.21468/scipostphys.10.6.154 ◽

2021 ◽

Vol 10 (6) ◽

Author(s):

Ketan Patel

Keyword(s):

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Fermion Mass ◽

Order Unity ◽

Anomaly Cancellation ◽

Fundamental Parameters ◽

Yukawa Couplings ◽

Fifth Dimension ◽

Fermion Masses ◽

The Masses

A mechanism to generate realistic fermion mass hierarchies based on supersymmetric gauged U(1)_FU(1)F symmetry in flat five-dimensional (5D) spacetime is proposed. The fifth dimension is compactified on S^1/Z_2S1/Z2 orbifold. The standard model fermions charged under the extra abelian symmetry along with their superpartners live in the 5D bulk. Bulk masses of fermions are generated by the vacuum expectation value of N=2N=2 superpartner of U(1)_FU(1)F gauge field, and they are proportional to U(1)_FU(1)F charges of respective fermions. This decides localization of fermions in the extra dimension, which in turn gives rise to exponentially suppressed Yukawa couplings in the effective 4D theory. Anomaly cancellation puts stringent constraints on the allowed U(1)_FU(1)F charges which leads to correlations between the masses of quarks and leptons. We perform an extensive numerical scan and obtain several solutions for anomaly-free U(1)_FU(1)F, which describe the observed pattern of fermion masses and mixing with all the fundamental parameters of order unity. It is found that the possible existence of SM singlet neutrinos substantially improves the spectrum of solutions by offering more freedom in choosing U(1)_FU(1)F charges. The model predicts Z^\primeZ′ boson mediating flavour violating interactions in both the quark and lepton sectors with the couplings which can be explicitly determined from the Yukawa couplings.

Download Full-text