133 research outputs found
Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
We construct, generalizing appropriately the method applied by J. Teschner in
the case of the Virasoro conformal blocks, the braiding and fusion matrices of
the Neveu-Schwarz super-conformal blocks. Their properties allow for an
explicit verification of the bootstrap equation in the NS sector of the N=1
supersymmetric Liouville field theory.Comment: 41 pages, 3 eps figure
Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability
We find the N-soliton solution at infinite theta, as well as the metric on
the moduli space corresponding to spatial displacements of the solitons. We use
a perturbative expansion to incorporate the leading 1/theta corrections, and
find an effective short range attraction between solitons. We study the
stability of various solutions. We discuss the finite theta corrections to
scattering, and find metastable orbits. Upon quantization of the two-soliton
moduli space, for any finite theta, we find an s-wave bound state.Comment: Second revision: Discussions of translation zero-modes in section 4
and scales in section 5 improved; web addresses of movies changed. First
revision: Section 6 is rewritten (thanks to M. Headrick for pointing out a
mistake in the original version); some references and acknowledgements added.
21 pages, JHEP style, Hypertex, 1 figure, 3 MPEG's at:
http://www.physto.se/~unge/traj1.mpg http://www.physto.se/~unge/traj2.mpg
http://www.physto.se/~unge/traj3.mp
Ground state energy of the modified Nambu-Goto string
We calculate, using zeta function regularization method, semiclassical energy
of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in
the action and discuss the tachyonic ground state problem.Comment: 10 pages, LaTeX, 2 figure
Classical conformal blocks from TBA for the elliptic Calogero-Moser system
The so-called Poghossian identities connecting the toric and spherical
blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for
the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain
expressions for the classical 4-point block on the sphere. The main motivation
for this line of research is the longstanding open problem of uniformization of
the 4-punctured Riemann sphere, where the 4-point classical block plays a
crucial role. It is found that the obtained representation for certain 4-point
classical blocks implies the relation between the accessory parameter of the
Fuchsian uniformization of the 4-punctured sphere and the eCMY functional.
Additionally, a relation between the 4-point classical block and the ,
twisted superpotential is found and further used to re-derive the
instanton sector of the Seiberg-Witten prepotential of the , supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio
Recursive representation of the torus 1-point conformal block
The recursive relation for the 1-point conformal block on a torus is derived
and used to prove the identities between conformal blocks recently conjectured
by R. Poghossian. As an illustration of the efficiency of the recurrence method
the modular invariance of the 1-point Liouville correlation function is
numerically analyzed.Comment: 14 pages, 1 eps figure, misprints corrected and a reference adde
Liouville theory and uniformization of four-punctured sphere
Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the
4-point classical Liouville action in terms of the 3-point actions and the
classical conformal block. In this paper we develop a method of calculating the
uniformizing map and the uniformizing group from the classical Liouville action
on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture
for an explicit construction of the uniformizing map and the uniformizing group
for the sphere with four punctures.Comment: 17 pages, no figure
Airy structures for semisimple Lie algebras
We give a complete classification of Airy structures for finite-dimensional
simple Lie algebras over , and to some extent also over ,
up to isomorphisms and gauge transformations. The result is that the only
algebras of this type which admit any Airy structures are ,
and . Among these, each admits exactly
two non-equivalent Airy structures. Our methods apply directly also to
semisimple Lie algebras. In this case it turns out that the number of
non-equivalent Airy structures is countably infinite. We have derived a number
of interesting properties of these Airy structures and constructed many
examples. Techniques used to derive our results may be described, broadly
speaking, as an application of representation theory in semiclassical analysis.Comment: Some references were adde
Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
Inspired by the work of Alday, Gaiotto and Tachikawa (AGT), we saw the
revival of Poincar{\'{e}}'s uniformization problem and Fuchsian equations
obtained thereof.
Three distinguished aspects are possessed by Fuchsian equations. First, they
are available via imposing a classical Liouville limit on level-two null-vector
conditions. Second, they fall into some A_1-type integrable systems. Third, the
stress-tensor present there (in terms of the Q-form) manifests itself as a kind
of one-dimensional "curve".
Thereby, a contact with the recently proposed Nekrasov-Shatashvili limit was
soon made on the one hand, whilst the seemingly mysterious derivation of
Seiberg-Witten prepotentials from integrable models become resolved on the
other hand. Moreover, AGT conjecture can just be regarded as a quantum version
of the previous Poincar{\'{e}}'s approach.
Equipped with these observations, we examined relations between spheric and
toric (classical) conformal blocks via Calogero-Moser/Heun duality. Besides, as
Sutherland model is also obtainable from Calogero-Moser by pinching tori at one
point, we tried to understand its eigenstates from the viewpoint of toric
diagrams with possibly many surface operators (toric branes) inserted. A
picture called "bubbling pants" then emerged and reproduced well-known results
of the non-critical self-dual c=1 string theory under a "blown-down" limit.Comment: 17 pages, 4 figures; v2: corrections and references added; v3:
Section 2.4.1 newly added thanks to JHEP referee advice. That classical
four-point spheric conformal blocks reproducing known SW prepotentials is
demonstrated via more examples, to appear in JHEP; v4: TexStyle changed onl
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