Constrained Hybrid Monte Carlo algorithms for gauge-Higgs models
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We present the construction of Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge-Higgs models in order to measure the constraint effective Higgs potential. In particular we focus on SU(2) Gauge-Higgs Unification models in five dimensions, where the Higgs field is identified with (some of) the five-dimensional components of the gauge field. Previous simulations have identified regions in the Higgs phase of these models which have properties of 4D adjoint or Abelian gauge-Higgs models. We develop new methods to measure constraint effective potentials, using an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian gauge-Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold. The derivative of the potential is determined via the expectation value of the Lagrange multiplier for the constraint. To our knowledge, this is the first time this problem has been addressed for theories with gauge fields. The algorithm can also be used in four dimensions to study finite temperature and density transitions via effective Polyakov loop actions.
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