The holographic non-abelian vortex

We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find, in the classical approximation in the bulk, a gapless $\mathbb{CP}^1$ excitation on the vortex world line.Comment: 28 pages, 7 figure

Trace anomaly for non-relativistic fermions

We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion to a curved Newton-Cartan geometry, using null reduction from an extra-dimensional relativistic Dirac action in curved spacetime. We analyze Weyl invariance in detail: we show that at the classical level it is preserved in an arbitrary curved background, whereas at the quantum level it is broken by anomalies. We compute the trace anomaly using the Heat Kernel method and we show that the anomaly coefficients a, c are proportional to the relativistic ones for a Dirac fermion in 3+1 dimensions. As for the previously studied scalar case, these coefficents are proportional to 1/m, where m is the non-relativistic mass of the particle.Comment: 23 page

Monopoles Can be Confined by 0, 1 or 2 Vortices

There are three types of monopole in gauge theories with fundamental matter and N=2 supersymmetry broken by a superpotential. There are unconfined 0-monopoles and also 1 and 2-monopoles confined respectively by one or two vortices transforming under distinct components of the unbroken gauge group. If a Fayet-Iliopoulos term is added then there are only 2-monopoles. Monopoles transform in the bifundamental representation of two components of the unbroken gauge symmetry, and if two monopoles share a component they may form a boundstate. Selection rules for this process are found, for example vortex number is preserved modulo 2. We find the tensions of the vortices, which are in general distinct, and also the conditions under which vortices are mutually BPS. Results are derived in field theory and also in MQCD, and in quiver theories a T-dual picture may be used in which monopoles are classified by quiver diagrams with two colors of vertices.Comment: 46 pages, 13 figures, V2: Comment on non-BPS correction added; 1 figure adde

Nonrelativistic trace and diffeomorphism anomalies in particle number background

Using the heat kernel method, we compute nonrelativistic trace anomalies for Schr\"odinger theories in flat spacetime, with a generic background gauge field for the particle number symmetry, both for a free scalar and a free fermion. The result is genuinely nonrelativistic, and it has no counterpart in the relativistic case. Contrary to the naive expectations, the anomaly is not gauge-invariant; this is similar to the non-gauge covariance of the non-abelian relativistic anomaly. We also show that, in the same background, the gravitational anomaly for a nonrelativistic scalar vanishes.Comment: 20 pages; V2 minor changes also in title, typo

Fractional and semi-local non-Abelian Chern-Simons vortices

In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U(1) x SO(2M) and G = U(1) x USp(2M) theories. The master equations are solved numerically using appropriate Ansatze for the moduli matrix field. In the fractional case the vortices are solved in the transverse plane due to the broken axial symmetry of the configurations (i.e. they are non-rotational invariant). It is shown that unless the fractional vortex-centers are all coincident (i.e. local case) the ring-like flux structure, characteristic of Chern-Simons vortices, will become bell-like fluxes - just as those of the standard Yang-Mills vortices. The asymptotic profile functions are calculated in all cases and the effective size is identified.Comment: LaTeX, 38 pages, 16 figures

New Results on Non-Abelian Vortices - further insights into monopole, vortex and confinement

We discuss some of the latest results concerning the non-Abelian vortices. The first concerns the construction of non-Abelian BPS vortices based on general gauge groups of the form G= G' x U(1). In particular detailed results about the vortex moduli space have been obtained for G'=SO(N) or USp(2N). The second result is about the "fractional vortices", i.e., vortices of the minimum winding but having substructures in the tension (or flux) density in the transverse plane. Thirdly, we discuss briefly the monopole-vortex complex.Comment: Latex 20 page

Hidden Modulus in the Extended Veneziano-Yankielowicz Theory

The issue of domain walls in the recently extended Veneziano-Yankielowicz theory is investigated and we show that they have an interesting substructure. We also demonstrate the presence of a noncompact modulus. The associated family of degenerate solutions is physically due to the presence of a valley of vacua in the enlarged space of fields. This is a feature of the extended Veneziano-Yankielowicz theory. Unfortunately the above properties do not match the ones expected for the domain walls of N=1 super Yang-Mills.Comment: LaTeX, 13 pages and 5 figs, v3 misprints correcte

Heat kernel for Newton-Cartan trace anomalies

We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.Comment: 18 page