35,245 research outputs found
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
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
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
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