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Register a new userOn the removal of the trace mode in lattice ${cal N}=4$ super Yang-Mills theory
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Twisted and orbifold formulations of lattice ${cal N}=4$ super Yang-Mills theory which possess an exact supersymmetry require a $U(N)=SU(N)otimes U(1)$ gauge group. In the naive continuum limit, the $U(1)$ modes trivially decouple and play no role in the theory. However, at non-zero lattice spacing they couple to the $SU(N)$ modes and can drive instabilities in the lattice theory. For example, it is well known that the lattice $U(1)$ theory undergoes a phase transition at strong coupling to a chirally broken phase. An improved action that suppresses the fluctuations in the $U(1)$ sector was proposed in arXiv:1505.03135 . Here, we explore a more aggressive approach to the problem by adding a term to the action which can entirely suppress the $U(1)$ mode. The penalty is that the new term breaks the $mathcal{Q}$-exact lattice supersymmetry. However, we argue that the term is $1/N^2$ suppressed and the existence of a supersymmetric fixed point in the planar limit ensures that any SUSY-violating terms induced in the action possess couplings that also vanish in this limit. We present numerical results on supersymmetric Ward identities consistent with this conclusion.
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Non-perturbative investigations of $mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
We derive a generalised concavity condition for potentials between static sources obtained from Wilson loops coupling both to gauge bosons and a set of scalar fields. It involves the second derivatives with respect to the distance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretical condition as a nontrivial consistency check of the AdS/CFT duality.
We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.
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