703 research outputs found
Plane Partition Realization of (Web of) W-algebra Minimal Models
Recently, Gaiotto and Rapcak (GR) proposed a new family of the vertex
operator algebra (VOA) as the symmetry appearing at an intersection of
five-branes to which they refer as Y algebra. Prochazka and Rapcak, then
proposed to interpret Y algebra as a truncation of affine Yangian whose module
is directly connected to plane partitions (PP). They also developed GR's idea
to generate a new VOA by connecting plane partitions through an infinite leg
shared by them and referred it as the web of W-algebra (WoW). In this paper, we
demonstrate that double truncation of PP gives the minimal models of such VOAs.
For a single PP, it generates all the minimal model irreducible representations
of W-algebra. We find that the rule connecting two PPs is more involved than
those in the literature when the U(1) charge connecting two PPs is negative.
For the simplest nontrivial WoW, N=2 superconformal algebra, we demonstrate
that the improved rule precisely reproduces the known character of the minimal
models.Comment: 37pages; references and minor comments added in 2nd versio
Holographic QCD Integrated back to Hidden Local Symmetry
We develop a previously proposed gauge-invariant method to integrate out
infinite tower of Kaluza-Klein (KK) modes of vector and axialvector mesons in a
class of models of holographic QCD (HQCD). The HQCD is reduced by our method to
the chiral perturbation theory with the hidden local symmetry (HLS) having only
the lowest KK mode identified as the HLS gauge boson. We take the
Sakai-Sugimoto model as a concrete HQCD, and completely determine the terms as well as the terms from the DBI part and the
anomaly-related (intrinsic parity odd) gauge-invariant terms from the CS part.
Effects of higher KK modes are fully included in these terms. To demonstrate
power of our method, we compute momentum-dependences of several form factors
such as the pion electromagnetic form factors, the - and
- transition form factors compared with experiment, which was
not achieved before due to complication to handle infinite sums. We also study
other anomaly-related quantities like --- and
--- vertex functions.Comment: 4 eps figures, 37 pages, latex, typos fixed; some discussions and
references added; fig.4 replace
(p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
Instanton partition functions of 5d Super Yang-Mills reduced
on can be engineered in type IIB string theory from the -branes
web diagram. To this diagram is superimposed a web of representations of the
Ding-Iohara-Miki (DIM) algebra that acts on the partition function. In this
correspondence, each segment is associated to a representation, and the
(topological string) vertex is identified with the intertwiner operator
constructed by Awata, Feigin and Shiraishi. We define a new intertwiner acting
on the representation spaces of levels , thereby
generalizing to higher rank the original construction. It allows us to use
a folded version of the usual -web diagram, bringing great
simplifications to actual computations. As a result, the characterization of
Gaiotto states and vertical intertwiners, previously obtained by some of the
authors, is uplifted to operator relations acting in the Fock space of
horizontal representations. We further develop a method to build qq-characters
of linear quivers based on the horizontal action of DIM elements. While
fundamental qq-characters can be built using the coproduct, higher ones require
the introduction of a (quantum) Weyl reflection acting on tensor products of
DIM generators.Comment: 42 page
pi+ pi0 Mass Difference in the Hidden Local Symmetry: A Dynamical Origin of Little Higgs
We calculate pi+ pi0 mass difference in the Hidden Local Symmetry (HLS) model, based on the Wilsonian
matching and Wilsonian renormalization-group equations. Even without a1 meson
the result agrees well with the experiment in sharp contrast to the
conventional approach where the a1 meson plays a crucial role. For large Nf
QCD, there arises a large hierarchy between and the pi decay
constant , , near the critical point
where the chiral symmetry gets restored as the vector manifestation and the HLS
model becomes a little Higgs model with two sites and two links, with the
dynamically generated gauge coupling of the composite rho becoming vanishingly
small.Comment: 4 page
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