We discuss gauge symmetry breaking in a general framework of gauge theories on an interval. We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements. It is shown that with these boundary conditions the scalar field can acquire a nontrivial vacuum expectation value even if the scalar mass square is positive. Any nonvanishing vacuum expectation value cannot be a constant but, in general, depends on the extra dimensional coordinate of the interval. The phase diagram of broken/unbroken gauge symmetry possesses a rich structure in the parameter space of the length of the interval, the scalar mass and the boundary conditions. We also discuss 4d chiral fermions and fermion mass hierarchies in our gauge symmetry breaking scenario.Comment: 16 pages, 8 figure

We study a 5d gravity theory with a warped metric and show that two N = 2 supersymmetric quantummechanical systems are hidden in the 4d spectrum. The supersymmetry can be regarded as a remnant of higherdimensional general coordinate invariance and turns out to become a powerful tool to determine the physical 4d spectrum and the allowed boundary conditions. Possible extensions of the N = 2 supersymmetry are briefly discussed.

h i g h l i g h t s• Supersymmetric quantum mechanics is an ideal playground for studying geometric phase.• We determine the parameter space of supersymmetric point-like interactions. • Berry's connection is given by a Wu-Yang-like magnetic monopole in SU(2) Yang-Mills. a b s t r a c tWe study non-Abelian geometric phase in N = 2 supersymmetric quantum mechanics for a free particle on a circle with two pointlike interactions at antipodal points. We show that non-Abelian Berry's connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule.

It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to fulfill some operator identities -the intertwining relations -in the representation space of conformal algebra. Meanwhile, it has been known that the S-matrix operator in scattering theory is nothing but the intertwining operator between the Hilbert spaces of in-and out-particles. Inspired by this algebraic resemblance, in this paper, we develop a simple Lie-algebraic approach to momentum-space two-point functions of thermal CFT living on the hyperbolic space-time H 1 × H d−1 by exploiting the idea of Kerimov's intertwining operator approach to exact S-matrix. We show that in thermal CFT on H 1 × H d−1 , the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. By solving these recurrence relations, we obtain the momentum-space representations of advanced and retarded two-point functions as well as positive-and negative-frequency two-point Wightman functions for a scalar primary operator in arbitrary space-time dimension d ≥ 3.

In this paper we study path integral for a single spinless particle on a star graph with N edges, whose vertex is known to be described by U (N ) family of boundary conditions. After carefully studying the free particle case, both at the critical and off-critical levels, we propose a new path integral formulation that correctly captures all the scale-invariant subfamily of boundary conditions realized at fixed points of boundary renormalization group flow. Our proposal is based on the folding trick, which maps a scalar-valued wave function on star graph to an N -component vector-valued wave function on halfline. All the parameters of scale-invariant subfamily of boundary conditions are encoded into the momentum independent weight factors, which appear to be associated with the two distinct path classes on half-line that form the cyclic group Z 2 . We show that, when bulk interactions are edge-independent, these weight factors are generally given by an N -dimensional unitary representation of Z 2 . Generalization to momentum dependent weight factors and applications to worldline formalism are briefly discussed.