ID: 2112.14765

Cobordism and Deformation Class of the Standard Model

December 29, 2021

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Pavel Putrov, Juven Wang
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In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf L$ number symmetry is free of mixed anomalies with strong and electroweak $su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces. However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent to leptogenesis in the very early universe. This happens when the total "sterile right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number $N_f$. Thus the inverti...

Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew

December 31, 2019

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Zheyan Wan, Juven Wang
Superconductivity
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We explore QCD$_4$ quark matter, the $\mu$-T (chemical potential-temperature) phase diagram, possible 't Hooft anomalies, and topological terms, via non-perturbative tools of cobordism theory and higher anomaly matching. We focus on quarks in 3-color and 3-flavor on bi-fundamentals of SU(3), then analyze the continuous and discrete global symmetries and pay careful attention to finite group sectors. We input constraints from $T=CP$ or $CT$ time-reversal symmetries, implementi...

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Proton Stability: From the Standard Model to Beyond Grand Unification

April 18, 2022

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Juven Wang, Zheyan Wan, Yi-Zhuang You
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A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ f...

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Smooth generalized symmetries of quantum field theories

October 24, 2023

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Ben Gripaios, Oscar Randal-Williams, Joseph Tooby-Smith
Algebraic Topology
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Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of $\infty$-categories. According to a geometric version of the cobordism hypothesis, such QFTs collectively assemble themselves into objects in an $\infty$-topos of smooth spaces. We show how this allows one to define and study generalized global symmetries of ...

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Gauge Enhanced Quantum Criticality Beyond the Standard Model

June 30, 2021

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Juven Wang, Yi-Zhuang You
Strongly Correlated Electron...

Standard lore views our 4d quantum vacuum governed by one of the candidate Standard Models (SMs), while lifting towards some Grand Unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an alternative view that the SM arises from various neighbor vacua competition in a quantum phase diagram. In general, we regard the SM arising near the gapless quantum criticality (either critical points or critical regions) between the competing neig...

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Anomalies in the Space of Coupling Constants and Their Dynamical Applications I

May 22, 2019

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Clay Cordova, Daniel S. Freed, ... , Seiberg Nathan
Strongly Correlated Electron...
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It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e} symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects 't Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study t...

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Global Anomalies on the Hilbert Space

January 6, 2021

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Diego Delmastro, Davide Gaiotto, Jaume Gomis
Strongly Correlated Electron...

We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology "layers" that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and s...

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Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms

December 31, 2018

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Meng Guo, Kantaro Ohmori, Pavel Putrov, ... , Wang Juven
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We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging $G$-equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a finite group $G$ symmetry. We use the fact that the latter are classified by Pontryagin duals to spin-bordism groups of the classifying space $BG$. We also cons...

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The Standard Model from String Theory: What Have We Learned?

January 3, 2024

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Fernando Marchesano, Gary Shiu, Timo Weigand
High Energy Physics - Theory
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Amidst all candidates of physics beyond the Standard Model, string theory provides a unique proposal for incorporating gauge and gravitational interactions. In string theory, a four-dimensional theory that unifies quantum mechanics and gravity is obtained automatically if one posits that the additional dimensions predicted by the theory are small and curled up, a concept known as compactification. The gauge sector of the theory is specified by the topology and geometry of the...

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Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop

February 27, 2017

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Gabriele Honecker, Isabel Koltermann, Wieland Staessens
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We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on the toroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes wrapping special Lagrangian cycles. To this aim, we employ the hypersurface formalism developed previously for the orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$ with discrete torsion and adapt it to the $\mathbb{Z}_2\times\mathbb{Z}_6\time...

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