40 research outputs found
Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical
potential with three quark flavours. Chiral and deconfinement phase transitions
are discussed, and the relevant order-like parameters are analyzed. The results
are compared with simple thermodynamic expectations and lattice data. A special
attention is payed to the critical end point: as the strength of the
flavour-mixing interaction becomes weaker, the critical end point moves to low
temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement
and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201
Moduli of symplectic instanton vector bundles of higher rank on projective space P3
Symplectic instanton vector bundles on the projective space P3 constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space In,r of rank-2r symplectic instanton vector bundles on P3 with r 65 2 and second Chern class n 65 r, n 61 r(mod2). We give an explicit construction of an irreducible component In 17,r of this space for each such value of n and show that In 17,r has the expected dimension 4n(r + 1) 12 r(2r + 1). \ua9 2012 Versita Warsaw and Springer-Verlag Wien
Special values of canonical Green's functions
We give a precise formula for the value of the canonical Green's function at
a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we
express the 'energy' of the Weierstrass points in terms of a spectral invariant
recently introduced by N. Kawazumi and S. Zhang. It follows that the energy is
strictly larger than log 2. Our results generalize known formulas for elliptic
curves.Comment: 10 page
The hypertoric intersection cohomology ring
We present a functorial computation of the equivariant intersection
cohomology of a hypertoric variety, and endow it with a natural ring structure.
When the hyperplane arrangement associated with the hypertoric variety is
unimodular, we show that this ring structure is induced by a ring structure on
the equivariant intersection cohomology sheaf in the equivariant derived
category. The computation is given in terms of a localization functor which
takes equivariant sheaves on a sufficiently nice stratified space to sheaves on
a poset.Comment: Significant revisions in Section 5, with several corrected proof
C^2/Z_n Fractional branes and Monodromy
We construct geometric representatives for the C^2/Z_n fractional branes in
terms of branes wrapping certain exceptional cycles of the resolution. In the
process we use large radius and conifold-type monodromies, and also check some
of the orbifold quantum symmetries. We find the explicit Seiberg-duality which
connects our fractional branes to the ones given by the McKay correspondence.
We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of
Harvey-Moore BPS algebras update
The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
We apply ideas that have appeared in the study of D-branes on Calabi-Yau
compactifications to the derivation of the BPS spectrum of field theories. In
particular, we identify an orbifold point whose fractional branes can be
thought of as ``partons'' of the BPS spectrum of N=2 pure SU(N) SYM. We derive
the BPS spectrum and lines of marginal stability branes near that orbifold, and
compare our results with the spectrum of the field theories.Comment: 29 pages, 4 figures, includes package diagrams.tex by Paul Taylo
Cyclotomic Gaudin models: construction and Bethe ansatz
This is a pre-copyedited author produced PDF of an article accepted for publication in Communications in Mathematical Physics, Benoit, V and Young, C, 'Cyclotomic Gaudin models: construction and Bethe ansatz', Commun. Math. Phys. (2016) 343:971, first published on line March 24, 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2601-3 © Springer-Verlag Berlin Heidelberg 2016To any simple Lie algebra and automorphism we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case . We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.Peer reviewe
Solving loop equations by Hitchin systems via holography in large-N QCD_4
For (planar) closed self-avoiding loops we construct a "holographic" map from
the loop equations of large-N QCD_4 to an effective action defined over
infinite rank Hitchin bundles. The effective action is constructed densely
embedding Hitchin systems into the functional integral of a partially quenched
or twisted Eguchi-Kawai model, by means of the resolution of identity into the
gauge orbits of the microcanonical ensemble and by changing variables from the
moduli fields of Hitchin systems to the moduli of the corresponding holomorphic
de Rham local systems. The key point is that the contour integral that occurs
in the loop equations for the de Rham local systems can be reduced to the
computation of a residue in a certain regularization. The outcome is that, for
self-avoiding loops, the original loop equations are implied by the critical
equation of an effective action computed in terms of the localisation
determinant and of the Jacobian of the change of variables to the de Rham local
systems. We check, at lowest order in powers of the moduli fields, that the
localisation determinant reproduces exactly the first coefficient of the beta
function.Comment: 65 pages, late
Fundamental solutions of the equations of quantum mechanics as distributions and distinctive properties of the Dirac equation solutions
We show that the causal Green's functions for interacting particles in external fields in both relativistic quantum mechanics (for the Dirac electron) and nonrelativistic quantum mechanics can be obtained as distributions if the free-particle Green's functions are used and equations for the corresponding test functions are chosen. We study quantum properties of solutions of the Dirac equations. © Springer Science+Business Media, Inc. 2007