We describe the electromagnetic field by the massless limit of a massive vector field in the presence of a Coulomb gauge fixing term. The gauge fixing term ensures that, in the massless limit, the longitudinal mode is removed from the spectrum and on
ly the two transverse modes survive. The system, coupled to a classical conserved current, is quantized in the canonical formalism. The classical field configurations due to time-independent electric charges and currents are represented by coherent states of longitudinal and transverse photons, respectively. The occupation number in these states is finite. In particular, the number of longitudinal photons bound by an electric charge q is given by N=q^2/(16pihbar).
The Polyakov loop of an operator in the anti-symmetric representation in N=4 SYM theory on spacial R^3 is calculated, to leading order in 1/N and at large t Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity m
odel. Agreement is found with previous results from the supergravity dual, which is given by a D5-brane in an asymptotically AdS_5 x S^5 black brane background. It is shown that the azimuth angle, at which the dual D5-brane wraps the S^5, is related to the spectral asymmetry angle in the spectral density associated with the Greens function of the impurity fermions. Much of the calculation also applies to the Polyakov loop on spacial S^3 or H^3.
Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The formula is che
cked for some simple examples from the AdS/CFT correspondence, but can be applied also in non-AdS/non-CFT cases.
The spectrum of two-point functions in a holographic renormalization group flow from an ultraviolet (UV) to an infrared (IR) conformal fixed point is necessarily continuous. For a toy model, the spectral function does not only show the expected UV an
d IR behaviours, but other interesting features such as sharp peaks and oscillations in the UV. The spectral functions for the SU(3)xU(1) flow in AdS_4/CFT_3 and the SU(2)xU(1) flow in AdS_5/CFT_4 are calculated numerically. They exhibit a simple cross-over behaviour and reproduce the conformal dimensions of the dual operators in the UV and IR conformal phases.
The generalization of Cohen and Glashows Very Special Relativity to curved space-times is considered. Gauging the SIM(2) symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2) invariant Lagrangian
s can always be constructed. For space-times with SIM(2) holonomy, they describe chiral fermions propagating freely as massive particles.
Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.
