Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

On the alleged equivalence of certain field theories

Abstract. We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.

Solitons of Coupled Scalar Field Theories in Two Dimensions

This work offers a method for finding some exact soliton solutions to coupled relativistic scalar field theories in 1+1 dimensions. The method can yield static solutions as well as quasistatic "charged" solutions for a variety of Lagrangians. Explicit solutions are derived as examples. A particularly interesting class of solutions is nontopological without being either charged or time dependent.

Path integral quantisation of topological field theories

Conditions for quantum topological invariance of classically topological field theories in the path integral formulation are discussed. Both the three-dimensional Chern-Simons system and a Witten-type topological field theory are shown to satisfy these conditions.

Mean-field theories of Hubbard and t-J models

We report novel results obtained for the Hubbard and t-J models by various mean-field approximations.

Renormalization of noncommutative quantum field theories

We report on a comprehensive analysis of the renormalization of noncommutative phi(4) scalar field theories on the Groenewold-Moyal plane. These scalar field theories are twisted Poincare invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative Lehmann-Symanzik-Zimmermann formalism. DOI: 10.1103/PhysRevD.87.064014

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

On states, on a lattice, with half-integral charge

In certain molecular models, and related one-dimensional field theories, localized objects appear with half-integral expectation values of charge. We consider whether these states are eigenstates of charge, with half-integral eigenvalue. We find that it is indeed so for a suitably diffuse definition of the charge operator in question. This diffuse charge operator has a spectrum which approaches a continuum. The analysis is made on a lattice, to avoid divergence ambiguities, and on a finite length, which is only subsequently made large. The half-integral charge phenomenon is not tied to solitons, but can also arise as an end effect.

Hydrodynamics from the D1-brane

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4 pi. This ratio continues to be 1/4 pi also in the regime when the D1-brane Yang-Mills theory is dual to the gravitational background of the fundamental string. Our analysis shows that this ratio is equal to 1/4 pi for a class of gravitational backgrounds dual to field theories in 1+1 dimensions obtained by considering D1-branes at cones over Sasaki-Einstein 7-manifolds.

Quantum supersymmetric generalisation of Bogomolnyi bounds

We review here classical Bogomolnyi bounds, and their generalisation to supersymmetric quantum field theories by Witten and Olive. We also summarise some recent work by several people on whether such bounds are saturated in the quantised theory.

Effect of Polymer Grafting on the Bilayer Gel to Liquid-Crystalline Transition

Grafted polymers oil the surface of lipid membranes have potential applications in liposome-based drug delivery and Supported membrane systems. The effect of polymer grafting on the phase behavior of bilayers made up of single-tail lipids is investigated using dissipative particle dynamics. The bilayer is maintained in a tensionless state using a barostat. Simulations are carried Out by varying the grafting fraction, G(f), defined as the ratio of the number of polymer molecules to the number of lipid molecules, and the length of the lipid tails. At low G(f), the bilayer shows I sharp transition from the gel (L-beta) to the liquid-crystalline (L-alpha) phase. This main melting transition temperature is lowered as G(f) is increased, and above a critical value of G(f), the interdigitated L-beta I phase is observed prior to the main transition. The temperature range over which the intermediate phases are observed is a function of the lipid tail length and G(f). At higher grafting fractions, the presence of the L-beta I, phase is attributed to the increase in the area per head group due to the lateral pressure exerted by the polymer brush. The areal expansion and decrease in the melting temperatures as a function of G(f) were found to follow the scalings predicted by the self-consistent mean field theories for grafted polymer membranes. Our study shows that the grafted polymer density can be used to effectively control the temperature range and occurrence of a given bilayer phase.

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Melting and mechanical properties of polymer grafted lipid bilayer membranes

The influence of polymer grafting on the phase behavior and elastic properties of two tail lipid bilayers have been investigated using dissipative particle dynamics simulations. For the range of polymer lengths studied, the L(c) to L(alpha) transition temperature is not significantly affected for grafting fractions, G(f) between 0.16 and 0.25. A decrease in the transition temperature is observed at a relatively high grafting fraction, G(f) = 0.36. At low temperatures, a small increase in the area per head group, a(h), at high G(f) leads to an increase in the chain tilt, inducing order in the bilayer and the solvent. The onset of the phase transition occurs with the nucleation of small patches of thinned membrane which grow and form continuous domains as the temperature increases. This region is the co-existence region between the L(beta)(thick) and the L(alpha)(thin) phases. The simulation results for the membrane area expansion as a function of the grafting density conform extremely well to the scalings predicted by self-consistent mean field theories. We find that the bending modulus shows a small decrease for short polymers (number of beads, N(p) = 10) and low G(f), where the influence of polymer is reduced when compared to the effect of the increased a(h). For longer polymers (N(p) > 15), the bending modulus increases monotonically with increase in grafted polymer. Using the results from mean field theory, we partition the contributions to the bending modulus from the membrane and the polymer and show that the dominant contribution to the increased bending modulus arises from the grafted polymer. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3631940]

Counterterms, critical gravity, and holography

We consider counterterms for odd dimensional holographic conformal field theories (CFTs). These counterterms are derived by demanding cutoff independence of the CFT partition function on S-d and S-1 x Sd-1. The same choice of counterterms leads to a cutoff independent Schwarzschild black hole entropy. When treated as independent actions, these counterterm actions resemble critical theories of gravity, i.e., higher curvature gravity theories where the additional massive spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these are theories where at least one of the central charges associated with the trace anomaly vanishes. Connections between these theories and logarithmic CFTs are discussed. For a specific choice of parameters, the theories arising from counterterms are nondynamical and resemble a Dirac-Born-Infeld generalization of gravity. For even dimensional CFTs, analogous counterterms cancel log-independent cutoff dependence.