One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory

Abstract

We study the one loop renormalisation of 4d $SU(N)$ Yang-Mills theory with $M$ adjoint representation scalar multiplets related by $O(M)$ symmetry. General $M$ are of field theoretic interest, and the 4d one loop beta function of the gauge coupling $g^2$ vanishes for the case $M=22$, which is intriguing for string theory. This case is related to D3 branes of critical bosonic string theory in $D=22+4=26$. An RG fixed point could have provided a definition for a purely bosonic AdS/CFT, but we show that scalar self-couplings $\lambda$ ruin one-loop conformal invariance in the large $N$ limit. There are real fixed flows (fixed points of $\lambda /g^2$) only for $M\ge 406$, rendering one-loop fixed points of the gauge coupling and scalar couplings incompatible. We develop and check an algebraic approach to the one-loop renormalisation group which we find to be characterised by a non-associative algebra of marginal couplings. In the large $N$ limit, the resulting RG flows typically suffer from strong coupling in both the ultraviolet and the infrared. Only for $M\ge 406$ fine-tuned solutions exist which are weakly coupled in the infrared.

arXiv comment22 pages, 3 figures

References in corpus (19)

• Bound States Of Strings And $p$-Branes
• 4d Conformal Field Theories and Strings on Orbifolds
• On Conformal Theories in Four Dimensions
• Walking, Weak first-order transitions, and Complex CFTs
• Asymptotic safety guaranteed
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• Large N limit of orbifold field theories
• Vacuum stability of asymptotically safe gauge-Yukawa theories
• Perturbative Search for Fixed Lines in Large N Gauge Theories
• A Non-supersymmetric Large N CFT from Type 0 String Theory
• Large N Field Theory and AdS Tachyons
• Perturbative Gauge Theory and Closed String Tachyons
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Effective potential in non-supersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes
• Closed String Tachyons, AdS/CFT, and Large N QCD
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Price of Asymptotic Safety
• Holographic Complex Conformal Field Theories
• The QCD $\beta$-function On The String Worldsheet