Novel phases in strongly coupled four-fermion theories

Abstract

We study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an SU (4)-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs-Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.

Testing the holographic principle using lattice simulations

“…Moving on to the detailed thermodynamic behavior, in the left panel of Fig. 3 we show the action density versus t for α = 2 lattice volumes 16 × 8 and 24 × 12 with gauge groups SU (12) and SU (16). For sufficiently large N the low-temperature regime of this plot should correspond to the D1 phase of the gravity dual.…”

“…The upshot of this new lattice construction is that it preserves a closed subalgebra of the supersymmetries at non-zero lattice spacing. Numerical studies of the four-dimensional theory are in progress [13][14][15][16][17][18][19], but are very expensive because of the large number of degrees of freedom. In this regard, lower-dimensional theories are more tractable and can be well-studied at large N.…”

Maximally supersymmetric Yang–Mills on the lattice

“…2 breaks an η → η + cI N shift symmetry and lifts the corresponding U(1) fermion zero mode. 9 The improved action therefore allows us to compute the pfaffian of D with fully periodic boundary conditions (BCs). This is not possible for the unimproved lattice action, which relies on the fermions' anti-periodic (thermal) temporal BCs to lift this zero mode.…”

“…We recently introduced a general method that can be applied to regulate these flat directions in a manner compatible with the Q supersymmetry. 9 The procedure is to deform the Q ηD…”

“…7,8 At the same time this work has also led to improvements of the lattice construction, in particular the development of a new procedure to regulate flat directions in a manner compatible with the Q supersymmetry. 9 Given the central role of N = 4 SYM in the AdS/CFT correspondence that relates it to quantum gravity, it is important to continue large-scale lattice investigations of the theory away from the regime of weak coupling and for arbitrary numbers of colors N . The recent progress, although significant, is only the beginning of this effort.…”