Phase structure of lattice $\mathcal{N}=4$ super Yang-Mills

Abstract

We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consistent with the existence of a single deconfined phase at all observed values of the bare coupling.

N=4supersymmetry on a space-time lattice

“…In this section we summarize the twisted theory and its transcription to the A * 4 lattice, some features of which will play important roles in the numerical results presented in Sections IV and V. Although most of the information in this section has already appeared in Refs. [1,7,8,18] among others (the new results in Section II C will be derived in a separate future publication [19]), we suspect that much of it is not yet common knowledge, which motivates this review.…”

“…[18], to stabilize numerical computations we regulate the flat directions by including in the lattice action a potential…”

“…We obtain the continuum limit by taking 1/L → 0, where L is the linear length of the lattice volume [18]. Since N = 4 SYM possesses a line of conformal fixed points, this continuum limit may be taken for any fixed value of the bare 't Hooft coupling λ lat .…”

Two-dimensional N $$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations

“…The two-dimensional N = (2, 2) gauge theory with two-index matter has the following form on the lattice 25) JHEP07 (2014)067 and…”

“…The next step is to extend this theory such that it becomes a supersymmetric quiver gauge theory with two nodes and 1 There also exist other complementary approaches to the problem of lattice supersymmetry [13][14][15][16][17][18][19][20][21][22]. 2 Several aspects of this theory have been explored numerically in the recent past [23][24][25][26][27][28][29][30] JHEP07 (2014)067 with gauge group SU(N c ) × SU(N f ). This can be achieved by replicating the continuum twisted theory and then changing the group representation of an appropriate subset of the field content of the theory from adjoint to the product representations (N c , N f ) and (N c , N f ), with N c and N f being the fundamental representations of SU(N c ) and SU(N f ) respectively.…”