Beyond Standard Models and Grand Unifications: anomalies, topological terms, and dynamical constraints via cobordisms
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Springer
Received: January 15, Revised: June 4, Accepted: June 8, Published: July 9,
2020 2020 2020 2020
Zheyan Wana,1 and Juven Wangb,c,2,3,4 a
Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, U.S.A. c School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, U.S.A. b
E-mail: [email protected], [email protected] Abstract: We classify and characterize fully all invertible anomalies and all allowed topological terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we mean the inclusion of (1) perturbative local anomalies captured by perturbative Feynman diagram loop calculations, classified by Z free classes, and (2) nonperturbative global anomalies, classified by finite group ZN torsion classes. Our work built from [31] fuses the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and Freed-Hopkins theorem. For example, we compute bordism groups ΩG d and their invertible topological field theory invariants, which characterize dd topological terms and (d − 1)d anomalies, protected by the following symmetry group G: Spin × SU(3)×SU(2)×U(1) for SM with q = 1, 2, 3, 6; Spin×Spin(n) Zq ZF 2
or Spin × Spin(n) for SO(10) or SO(18) GUT as n = 10, 18; Spin × SU(n) for GeorgiSpin×
SU(4)×(SU(2)×SU(2)) Zq 0 ZF 2
Glashow SU(5) GUT as n = 5; for Pati-Salam GUT as q 0 = 1, 2; and others. For SM with an extra discrete symmetry, we obtain new anomaly matching conditions of Z16 , Z4 and Z2 classes beyond the familiar Witten anomaly. Our approach offers an alternative view of all anomaly matching conditions built from the lower-energy (B)SM or GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape 1
https://orcid.org/0000-0002-2714-0578. https://orcid.org/0000-0001-9396-9010. 3 Corresponding author. 4 http://sns.ias.edu/∼juven/. 2
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)062
JHEP07(2020)062
Beyond Standard Models and Grand Unifications: anomalies, topological terms, and dynamical constraints via cobordisms
v.s. Swampland program, as bottom-up/top-down complements. Symmetries and anomalies provide constraints of kinematics, we further suggest constraints of quantum gauge dynamics, and new predictions of possible extended defects/excitations plus hidden BSM non-perturbative topological sectors. Keywords: Anomalies in Field and String Theories, Beyond Standard Model, Nonperturbative Effects, Topological States of Matter ArXiv ePrint: 1910.14668
JHEP07(2020)062
Contents 1 1 11 11 14 15 19 20
2 Standard models 2.1 Spin × SU(3) × SU(2) × U(1) model 2.2 Spin × SU(3)×SU(2)×U(1) model Z2
22 22 26
SU(3)×SU(2)×U(1) Z3 SU(3)×SU(2)×U(1) Z6
2.3
Spin ×
2.4 2.5
Spin × model Comparison between Adams spectral sequence and Atiyah-Hirzebruch spectral sequence
model
26
3 Standard Models wit
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