4,438 research outputs found
Schur Superpolynomials: Combinatorial Definition and Pieri Rule
Schur superpolynomials have been introduced recently as limiting cases of the
Macdonald superpolynomials. It turns out that there are two natural
super-extensions of the Schur polynomials: in the limit and
, corresponding respectively to the Schur
superpolynomials and their dual. However, a direct definition is missing. Here,
we present a conjectural combinatorial definition for both of them, each being
formulated in terms of a distinct extension of semi-standard tableaux. These
two formulations are linked by another conjectural result, the Pieri rule for
the Schur superpolynomials. Indeed, and this is an interesting novelty of the
super case, the successive insertions of rows governed by this Pieri rule do
not generate the tableaux underlying the Schur superpolynomials combinatorial
construction, but rather those pertaining to their dual versions. As an aside,
we present various extensions of the Schur bilinear identity
Expectation values of twist fields and universal entanglement saturation of the free massive boson
The evaluation of vacuum expectation values (VEVs) in massive integrable
quantum field theory (QFT) is a nontrivial renormalization-group "connection
problem" -- relating large and short distance asymptotics -- and is in general
unsolved. This is particularly relevant in the context of entanglement entropy,
where VEVs of branch-point twist fields give universal saturation predictions.
We propose a new method to compute VEVs of twist fields associated to
continuous symmetries in QFT. The method is based on a differential equation in
the continuous symmetry parameter, and gives VEVs as infinite form-factor
series which truncate at two-particle level in free QFT. We verify the method
by studying U(1) twist fields in free models, which are simply related to the
branch-point twist fields. We provide the first exact formulae for the VEVs of
such fields in the massive uncompactified free boson model, checking against an
independent calculation based on angular quantization. We show that logarithmic
terms, overlooked in the original work of Callan and Wilczek [Phys. Lett. B333
(1994)], appear both in the massless and in the massive situations. This
implies that, in agreement with numerical form-factor observations by Bianchini
and Castro-Alvaredo [Nucl. Phys. B913 (2016)], the standard power-law
short-distance behavior is corrected by a logarithmic factor. We discuss how
this gives universal formulae for the saturation of entanglement entropy of a
single interval in near-critical harmonic chains, including log log
corrections.Comment: V2: 37 pages, explications and references adde
The supersymmetric Ruijsenaars-Schneider model
An integrable supersymmetric generalization of the trigonometric
Ruijsenaars-Schneider model is presented whose symmetry algebra includes the
super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be
diagonalized by the recently introduced Macdonald superpolynomials. Somewhat
surprisingly, the consistency of the scalar product forces the discreteness of
the Hilbert space.Comment: v1: 11 pages, 1 figure. v2: new format, 5 pages, short section added
at the end of the article addressing the problem of consistency of the scalar
product (e.g., positivity of the weight functions and the normalization of
the ground state wave function). To appear in Physical Review Letter
A quartet of fermionic expressions for Virasoro characters via half-lattice paths
We derive new fermionic expressions for the characters of the Virasoro
minimal models by analysing the recently introduced half-lattice
paths. These fermionic expressions display a quasiparticle formulation
characteristic of the and integrable perturbations.
We find that they arise by imposing a simple restriction on the RSOS
quasiparticle states of the unitary models . In fact, four fermionic
expressions are obtained for each generating function of half-lattice paths of
finite length , and these lead to four distinct expressions for most
characters . These are direct analogues of Melzer's
expressions for , and their proof entails revisiting, reworking and
refining a proof of Melzer's identities which used combinatorial transforms on
lattice paths.
We also derive a bosonic version of the generating functions of length
half-lattice paths, this expression being notable in that it involves
-trinomial coefficients. Taking the limit shows that the
generating functions for infinite length half-lattice paths are indeed the
Virasoro characters .Comment: 29 pages. v2: minor improvements, references adde
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