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Register a new userRenormalizability of the Schrodinger Functional
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Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the divergences induced by these surface interactions can be absorbed by a renormalization of their coefficients.
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Walking technicolor theory attempts to realize electroweak symmetry breaking as the spontaneous chiral symmetry breakdown caused by the gauge dynamics with slowly varying gauge coupling constant and large mass anomalous dimension. Many-flavor QCD is one of the candidates owning these features. We focus on the SU(3) gauge theory with ten flavors of massless fermions in the fundamental representation, and compute the gauge coupling constant in the Schrodinger functional scheme. Numerical simulation is performed with $O(a)$-unimproved lattice action, and the continuum limit is taken in linear in lattice spacing. We observe evidence that this theory possesses an infrared fixed point.
We consider the Schrodinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are proposed, corresponding to the coarse lattice having size $(L/2a)^3 times (T/2a)$, with $T = T pm a$. The continuum limit is then defined at fixed $T/L$. Both cases have previously been investigated in the pure gauge theory. Here we define fermionic correlation functions and study their approach to the continuum limit at tree-level of perturbation theory.
The chirally rotated Schrodinger functional ($chi$SF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schrodinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O($a$) improvement to be operational in the $chi$SF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the $chi$SF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O($a$) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the $chi$SF framework and prepares the ground for non-perturbative applications.
The analysis developed by Luscher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration. We show for the $phi^4$ theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms. When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields $phi(x_i, t_i)$, $1le i le N $, corresponding to a specific 4-dimensional Feynman graph separates into two factors: one depending on the Monte-Carlo evolution times $t_i$ and the second depending on the space-time positions $x_i$. This separation implies that only auto-correlation times at the lattice scale appear, eliminating critical slowing down in perturbation theory.
The electroweak gauge symmetry is allowed to be spontaneously broken by the strongly interacting vector-like gauge dynamics. When the gauge coupling of a theory runs slowly in a wide range of energy scale, the theory is a candidate for walking technicolor. This may open up the possibility that the origin of all masses may be traced back to the gauge theory. We use the SF method to see whether the gauge coupling of 10-flavor QCD walks or not. Preliminary result is reported.
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