Gauge fixing the Standard Model Effective Field Theory

We gauge fix the Standard Model Effective Field Theory in a manner invariant under background field gauge transformations using a geometric description of the field connections.Comment: 4 pages. Accepted in PR

On the spectrum and string tension of U(1) lattice gauge theory in 2+1 dimensions

We calculate the low-lying spectra of glueballs and confining flux tubes in the U(1) lattice gauge theory in 2+1 dimensions. We see that up to modest lattice spacing corrections, the glueball states are consistent with being multiparticle states composed of non-interacting massive JPC=0-- particles. We observe that the ag^2 -> 0 limit is, as expected, unconventional, and follows the well-known saddle-point analysis of Polyakov to a good approximation. The spectrum of closed (winding) flux tubes exhibits the presence of a massive world-sheet excitation whose mass is consistent with that of the bulk screening mass. These U(1) calculations are intended to complement existing lattice calculations of the properties of SU(N) and SO(N) gauge theories in D=2+1.Comment: 39 pages; 15 figures. Extra discussion, calculation, figures and reference

Reverse mathematics and well-ordering principles

The paper is concerned with generally Pi^1_2 sentences of the form 'if X is well ordered then f(X) is well ordered', where f is a standard proof theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded omega-models for a particular theory T_f whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate this theme, we shall focus on the well-known psi-function which figures prominently in so-called predicative proof theory. However, the approach taken here lends itself to generalization in that the techniques we employ can be applied to many other proof-theoretic functions associated with cut elimination theorems. In this paper we show that the statement 'if X is well ordered then 'X0 is well ordered' is equivalent to ATR0. This was first proved by Friedman, Montalban and Weiermann [7] using recursion-theoretic and combinatorial methods. The proof given here is proof-theoretic, the main techniques being Schuette's method of proof search (deduction chains) [13], generalized to omega logic, and cut elimination for infinitary ramified analysis

Closed flux tubes in D=2+1 SU(N) gauge theories: dynamics and effective string description

We extend our earlier calculations of the spectrum of closed flux tubes in SU(N) gauge theories in 2+1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1/l^gamma) non-universal correction to the flux tube ground state energy does indeed have a power gamma greater than or equal to 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all-N view of the spectrum. Our comparison of the k=2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k=2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU(N) representations, which implies that their screening by gluons is highly suppressed even at small N.Comment: 72 pages, including 42 figure

On the mass of the world-sheet `axion' in SU(N) gauge theories in 3+1 dimensions

There is numerical evidence that the world sheet action of the confining flux tube in D=3+1 SU(N) gauge theories contains a massive excitation with 0- quantum numbers whose mass shows some decrease as one goes from SU(3) to SU(5). It has furthermore been shown that this particle is naturally described as arising from a topological interaction term in the world-sheet action, so that one can describe it as being `axion'-like. Recently it has been pointed out that if the mass of this `axion' vanishes as N -> oo then it becomes possible for the world sheet theory to be integrable in the planar limit. In this paper we perform lattice calculations of this `axion' mass from SU(2) to SU(12), which allows us to make a controlled extrapolation to N=oo and so test this interesting possibility. We find that the `axion' does not in fact become massless as N -> oo. So if the theory is to possess planar integrability then it must be some other world sheet excitation that becomes massless in the planar limit.Comment: 14 pages, 2 tables, 3 figures; some typos corrected plus minor clarification

A direct link between the quantum-mechanical and semiclassical determination of scattering resonances

We investigate the scattering of a point particle from n non-overlapping, disconnected hard disks which are fixed in the two-dimensional plane and study the connection between the spectral properties of the quantum-mechanical scattering matrix and its semiclassical equivalent based on the semiclassical zeta function of Gutzwiller and Voros. We rewrite the determinant of the scattering matrix in such a way that it separates into the product of n determinants of 1-disk scattering matrices - representing the incoherent part of the scattering from the n disk system - and the ratio of two mutually complex conjugate determinants of the genuine multi-scattering kernel, M, which is of Korringa-Kohn-Rostoker-type and represents the coherent multi-disk aspect of the n-disk scattering. Our result is well-defined at every step of the calculation, as the on-shell T-matrix and the kernel M-1 are shown to be trace-class. We stress that the cumulant expansion (which defines the determinant over an infinite, but trace class matrix) imposes the curvature regularization scheme to the Gutzwiller-Voros zeta function and thus leads to a new, well-defined and direct derivation of the semiclassical spectral function. We show that unitarity is preserved even at the semiclassical level.Comment: 23 pages, latex with IOP journal preprint style, no figures; final version - considerably shortene