# Quantum Critical Behaviour of Semisimple Gauge Theories

Jacob Kamuk Esbensen, Thomas A. Ryttov, Francesco Sannino

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

### Resumé

We study the perturbative phase diagram of semi-simple fermionic gauge theories resembling the Standard Model. We investigate an $SU(N)$ gauge theory with $M$ Dirac flavors where we gauge first an $SU(M)_L$ and then an $SU(2)_L \subset SU(M)_L$ of the original global symmetry $SU(M)_L\times SU(M)_R \times U(1)$ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalisation group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are \emph{safety free} trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics a l\'a walking is investigated.
Originalsprog Engelsk 045009 Physical Review D (Particles, Fields, Gravitation and Cosmology) 93 4 1-13 0556-2821 https://doi.org/10.1103/PhysRevD.93.045009 Udgivet - 2016

gauge theory
phase diagrams
trajectories
walking
safety
anomalies
symmetry

### Bibliografisk note

20 pages, 10 figures, 2 tables

### Citer dette

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title = "Quantum Critical Behaviour of Semisimple Gauge Theories",
abstract = "We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an SU{\dh}N{\TH} gauge theory with M Dirac flavors where we gauge first an SU{\dh}M{\TH}L and then an SU{\dh}2{\TH}L ⊂ SU{\dh}M{\TH}L of the original global symmetry SU{\dh}M{\TH}L × SU{\dh}M{\TH}R × U{\dh}1{\TH} of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedomand simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safetyfree trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics {\`a} la walking is investigated.",
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author = "{Kamuk Esbensen}, Jacob and Ryttov, {Thomas A.} and Francesco Sannino",
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Quantum Critical Behaviour of Semisimple Gauge Theories. / Kamuk Esbensen, Jacob; Ryttov, Thomas A.; Sannino, Francesco.

I: Physical Review D (Particles, Fields, Gravitation and Cosmology), Bind 93, Nr. 4, 045009, 2016, s. 1-13.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Quantum Critical Behaviour of Semisimple Gauge Theories

AU - Kamuk Esbensen, Jacob

AU - Ryttov, Thomas A.

AU - Sannino, Francesco

N1 - 20 pages, 10 figures, 2 tables

PY - 2016

Y1 - 2016

N2 - We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an SUðNÞ gauge theory with M Dirac flavors where we gauge first an SUðMÞL and then an SUð2ÞL ⊂ SUðMÞL of the original global symmetry SUðMÞL × SUðMÞR × Uð1Þ of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedomand simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safetyfree trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.

AB - We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an SUðNÞ gauge theory with M Dirac flavors where we gauge first an SUðMÞL and then an SUð2ÞL ⊂ SUðMÞL of the original global symmetry SUðMÞL × SUðMÞR × Uð1Þ of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedomand simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safetyfree trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.

KW - hep-th

KW - hep-lat

KW - hep-ph

U2 - 10.1103/PhysRevD.93.045009

DO - 10.1103/PhysRevD.93.045009

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SP - 1

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JO - Physical Review D. Particles and fields

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