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A resummable β-function for massless QED
Get PDFWithin the set of schemes defined by generalized, manifestly gauge invariant exact renormalization groups for QED, it is argued that the β-function in the four dimensional massless theory cannot possess any nonperturbative power corrections. Consequently, the perturbative expression for the β-function must be resummable. This argument cannot be extended to flows of the other couplings or to the anomalous dimension of the fermions and so perturbation theory does not define a unique trajectory in the critical surface of the Gaussian fixed point. Thus, resummability of the β-function is not inconsistent with the expectation that a non-trivial fixed point does not exist
From Vicious Walkers to TASEP
Get PDFWe propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for m particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For m particles its asymptotic behavior is shown to be e^(-(y^2)/(2m^2)) as y → −∞ and e^(-(y^2)/(2m))*y^(-(m(m-1))/2) as y → ∞
An ab initio Calculation of the Universal Equation of State for the O(N) Model
Get PDFUsing an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y = f(x), that exhibits all required analyticity properties in the limits x → 0, x → ∞ and x → −1. Unlike current methodologies based on a phenomenological scaling ansatz the scaling function is derived solely from the underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three Wilson functions γ_λ , γ_φ and γ_(φ^2) which exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the strong coupling fixed point associated with the Goldstone modes on the coexistence curve. We give explicit results for N = 2, 3 and 4 to one-loop order and compare with known results
On the Renormalization of Theories of a Scalar Chiral Superfield
Get PDFAn exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action, it is shown that the nonperturbative nonrenormalization theorem follows, quite simply, from the flow equation. Next, it is proven there do not exist any physically acceptable non-trivial fixed points. Finally, the Wess-Zumino model is considered, as a low energy effective theory. Following an evaluation of the one and two loop β-function coefficients, to illustrate the ease of use of the formalism, it is shown that the β-function in the massless case does not receive any nonperturbative power corrections
Topological Phase Transitions and Holonomies in the Dimer Model
Get PDFWe demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general bond activities we find that the phase transition in this model is a topological one where the modular parameter of the torus goes to zero at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion
The Irish of Iorras Aithneach, County Galway; Volume IV
Get PDFThis grammar is based on extensive fieldwork, published and unpublished lore, and recent as well as older recordings, particularly those held in the archives of Roinn Bhéaloideas Éireann and Raidió na Gaeltachta. These sources provide a picture of extensive variation and change across the six generations born between 1850 and 2000. The grammar draws on several branches of linguistics: descriptive and historical linguistics, dialectology and sociolinguistics. It is the most comprehensive treatment of any variety of Irish.
Volume IV presents transcriptions and a CD containing recordings of a slection of speakers across the generations. The final volume also contains a vocabulary, bibliography and four indexes
Classical Capacity of Quantum Channels with General Markovian Correlated Noise
Get PDFThe classical capacity of a quantum channel with arbitrary Markovian correlated noise is evaluated. For an irreducible and aperiodic Markov Chain, the channel is forgetful, and one retrieves the known expression [15] for the capacity. For the more general case of a channel with long-term memory, which corresponds to a Markov chain which does not converge to equilibrium, the capacity is expressed in terms of the communicating classes of the Markov chain
Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian
Get PDFThe hierarchy of conformally coupled scalars with the increasing scaling dimensions ∆_k = k − d/2, k = 1, 2, 3, . . . connected with the k-th Euler density in the corresponding space-time dimensions d ≥ 2k is proposed. The corresponding conformal invariant Lagrangian with the k-th power of Laplacian for the already known cases k = 1, 2 is reviewed, and the subsequent case of k = 3 is completely constructed and analyzed
Counting BPS operators in N = 4 SYM
Get PDFThe free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free N = 4 super Yang Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of N = 4 super Yang Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free N = 4 super Yang Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory