4,737 research outputs found
Comments on geometric and universal open string tachyons near fivebranes
In a recent paper (hep-th/0703157), Sen studied unstable D-branes in
NS5-branes backgrounds and argued that in the strong curvature regime the
universal open string tachyon (on D-branes of the wrong dimensionality) and the
geometric tachyon (on D-branes that are BPS in flat space but not in this
background) may become equivalent. We study in this note an example of a
non-BPS suspended D-brane vs. a BPS D-brane at equal distance between two
fivebranes. We use boundary worldsheet CFT methods to show that these two
unstable branes are identical.Comment: 8 pages, 1 figure; ver. 2 to appear in JHEP: one comment, refs and
appendices adde
Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories
We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2
SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting
from path-integral calculations of torus partition functions of both the
axial-type (`cigar') and the vector-type (`trumpet') models, we study general
models of the Z_M-orbifolds and M-fold covers with an arbitrary integer M. We
then extract contributions of the degenerate representations (`discrete
characters') in such a way that good modular properties are preserved. The
`modular completion' of the extended discrete characters introduced in
arXiv:1012.5721 [hep-th] are found to play a central role as suitable building
blocks in every model of orbifolds or covering spaces. We further examine a
large M-limit (the `continuum limit'), which `deconstructs' the spectral flow
orbits while keeping a suitable modular behavior. The discrete part of
partition function as well as the elliptic genus is then expanded by the
modular completions of irreducible discrete characters, which are parameterized
by both continuous and discrete quantum numbers modular transformed in a mixed
way. This limit is naturally identified with the universal cover of trumpet
model. We finally discuss a classification of general modular invariants based
on the modular completions of irreducible characters constructed above.Comment: 1+40 pages, no figure; v2 some points are clarified with respect to
the `continuum limit', typos corrected, to appear in JHEP; v3 footnotes added
in pages 18, 23 for the relation with arXiv:1407.7721[hep-th
Melting Crystal, Quantum Torus and Toda Hierarchy
Searching for the integrable structures of supersymmetric gauge theories and
topological strings, we study melting crystal, which is known as random plane
partition, from the viewpoint of integrable systems. We show that a series of
partition functions of melting crystals gives rise to a tau function of the
one-dimensional Toda hierarchy, where the models are defined by adding suitable
potentials, endowed with a series of coupling constants, to the standard
statistical weight. These potentials can be converted to a commutative
sub-algebra of quantum torus Lie algebra. This perspective reveals a remarkable
connection between random plane partition and quantum torus Lie algebra, and
substantially enables to prove the statement. Based on the result, we briefly
argue the integrable structures of five-dimensional
supersymmetric gauge theories and -model topological strings. The
aforementioned potentials correspond to gauge theory observables analogous to
the Wilson loops, and thereby the partition functions are translated in the
gauge theory to generating functions of their correlators. In topological
strings, we particularly comment on a possibility of topology change caused by
condensation of these observables, giving a simple example.Comment: Final version to be published in Commun. Math. Phys. . A new section
is added and devoted to Conclusion and discussion, where, in particular, a
possible relation with the generating function of the absolute Gromov-Witten
invariants on CP^1 is commented. Two references are added. Typos are
corrected. 32 pages. 4 figure
Superconformal Algebras and Mock Theta Functions
It is known that characters of BPS representations of extended superconformal
algebras do not have good modular properties due to extra singular vectors
coming from the BPS condition. In order to improve their modular properties we
apply the method of Zwegers which has recently been developed to analyze
modular properties of mock theta functions. We consider the case of N=4
superconformal algebra at general levels and obtain the decomposition of
characters of BPS representations into a sum of simple Jacobi forms and an
infinite series of non-BPS representations.
We apply our method to study elliptic genera of hyper-Kahler manifolds in
higher dimensions. In particular we determine the elliptic genera in the case
of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]}
and complex tori A^{[[3]]}.Comment: 28 page
Surface Shubnikov-de Hass oscillations and non-zero Berry phases of the topological hole conduction in TlBiSe
We report the observation of two-dimensional Shubnikov-de Hass (SdH)
oscillations in the topological insulator TlBiSe. Hall
effect measurements exhibited electron-hole inversion in samples with bulk
insulating properties. The SdH oscillations accompanying the hole conduction
yielded a large surface carrier density of /cm, with the Landau-level fan diagram exhibiting the
Berry phase. These results showed the electron-hole reversibility around the
in-gap Dirac point and the hole conduction on the surface Dirac cone without
involving the bulk metallic conduction.Comment: 5 pages, 4 figure
Seiberg-Witten Curve for the E-String Theory
We construct the Seiberg-Witten curve for the E-string theory in
six-dimensions. The curve is expressed in terms of affine E_8 characters up to
level 6 and is determined by using the mirror-type transformation so that it
reproduces the number of holomorphic curves in the Calabi-Yau manifold and the
amplitudes of N=4 U(n) Yang-Mills theory on 1/2 K3. We also show that our curve
flows to known five- and four-dimensional Seiberg-Witten curves in suitable
limits.Comment: 18 pages, 1 figure; appendix C adde
N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds
We study the elliptic genera of hyperKahler manifolds using the
representation theory of N=4 superconformal algebra. We consider the
decomposition of the elliptic genera in terms of N=4 irreducible characters,
and derive the rate of increase of the multiplicities of half-BPS
representations making use of Rademacher expansion. Exponential increase of the
multiplicity suggests that we can associate the notion of an entropy to the
geometry of hyperKahler manifolds. In the case of symmetric products of K3
surfaces our entropy agrees with the black hole entropy of D5-D1 system.Comment: 25 pages, 1 figur
Givental formula in terms of Virasoro operators
We present a conjecture that the universal enveloping algebra of differential
operators \frac{\p}{\p t_k} over coincides in the origin with
the universal enveloping algebra of the (Borel subalgebra of) Virasoro
generators from the Kontsevich model. Thus, we can decompose any
(pseudo)differential operator to a combination of the Virasoro operators. Using
this decomposition we present the r.h.s. of the Givental formula
math.AG/0008067 as a constant part of the differential operator we introduce.
In the case of studied in hep-th/0103254, the l.h.s. of the
Givental formula is a unit, which imposes certain constraints on this
differential operator. We explicitly check that these constraints are correct
up to . We also propose a conjecture of factorization modulo Hirota
equation of the differential operator introduced and check this conjecture with
the same accuracy.Comment: LaTeX, 11 pages, Some typos correcte
The non-compact elliptic genus: mock or modular
We analyze various perspectives on the elliptic genus of non-compact
supersymmetric coset conformal field theories with central charge larger than
three. We calculate the holomorphic part of the elliptic genus via a free field
description of the model, and show that it agrees with algebraic expectations.
The holomorphic part of the elliptic genus is directly related to an
Appell-Lerch sum and behaves anomalously under modular transformation
properties. We analyze the origin of the anomaly by calculating the elliptic
genus through a path integral in a coset conformal field theory. The path
integral codes both the holomorphic part of the elliptic genus, and a
non-holomorphic remainder that finds its origin in the continuous spectrum of
the non-compact model. The remainder term can be shown to agree with a function
that mathematicians introduced to parameterize the difference between mock
theta functions and Jacobi forms. The holomorphic part of the elliptic genus
thus has a path integral completion which renders it non-holomorphic and
modular.Comment: 13 page
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