1,015 research outputs found
Topological quantum field theory and four-manifolds
I review some recent results on four-manifold invariants which have been
obtained in the context of topological quantum field theory. I focus on three
different aspects: (a) the computation of correlation functions, which give
explicit results for the Donaldson invariants of non-simply connected
manifolds, and for generalizations of these invariants to the gauge group
SU(N); (b) compactifications to lower dimensions, and relations with
three-manifold topology and with intersection theory on the moduli space of
flat connections on Riemann surfaces; (c) four-dimensional theories with
critical behavior, which give some remarkable constraints on Seiberg-Witten
invariants and new results on the geography of four-manifolds.Comment: 10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000;
references adde
Softly Broken N=2 QCD with Massive Quark Hypermultiplets, I
We present a general analysis of all the possible soft breakings of N=2
supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten
solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all
the couplings of the spurion fields in terms of properties of the
Seiberg-Witten periods, which we express in terms of elementary elliptic
functions by uniformizing the elliptic curves associated to each number of
flavors. We analyze in detail the monodromy properties of the softly broken
theory, and obtain them by a particular embedding into a pure gauge theory with
higher rank group. This allows to write explicit expressions of the effective
potential, which are close to the exact answer for moderate values of the
supersymmetry breaking parameters. The vacuum structures and phases of the
broken theories will be analyzed in the forthcoming second part of this paper.Comment: 35 pages, 3 figures, LaTeX file. Minor corrections in a few formulae,
typos correcte
El embarazo precoz: no querido pero deseado / Early pregnancy: not wanted but wished for
En los últimos años la tasa de fecundidad global entre las mujeres adultas
ha descendido notablemente, en tanto entre las adolescentes se ha incrementado,
al decir de Matilde Maddaleno (1995) en un artículo para la Organización
Panamericana de la Salud; de igual manera opina Marcelo Dávalos (2006) al
manifestar que en el país ha descendido de 6,76 a 3,61 en el último medio siglo
anterior, en tanto que la “tasa de fecundidad especifica” de adolescentes en
América ha aumentado. De cuatro embarazos reportados uno es adolescente,
por lo que podríamos colegir que de cien embarazos, veinticinco son precoces
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
We develop techniques to compute multi-instanton corrections to the 1/N
expansion in matrix models described by orthogonal polynomials. These
techniques are based on finding trans-series solutions, i.e. formal solutions
with exponentially small corrections, to the recursion relations characterizing
the free energy. We illustrate this method in the Hermitian, quartic matrix
model, and we provide a detailed description of the instanton corrections in
the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel
resummation techniques and results from the theory of resurgent functions to
relate the formal multi-instanton series to the nonperturbative definition of
the matrix model. We study this relation in the case of the GWW model and its
double-scaling limit, providing in this way a nice illustration of various
mechanisms connecting the resummation of perturbative series to nonperturbative
results, like the cancellation of nonperturbative ambiguities. Finally, we
argue that trans-series solutions are also relevant in the context of
topological string theory. In particular, we point out that in topological
string models with both a matrix model and a large N gauge theory description,
the nonperturbative, holographic definition involves a sum over the
multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small
correction
UPC-BMIC-VDU system description for the IWSLT 2010: testing several collocation segmentations in a phrase-based SMT system
This paper describes the UPC-BMIC-VMU participation in the IWSLT 2010 evaluation campaign. The SMT system is a standard phrase-based enriched with novel segmentations. These novel segmentations are computed using statistical measures such as Log-likelihood, T-score, Chi-squared, Dice, Mutual Information or Gravity-Counts. The analysis of translation results allows to divide measures into three groups. First, Log-likelihood, Chi-squared and T-score tend to combine high frequency words and collocation segments are very short. They improve the SMT system by adding new translation units. Second, Mutual Information and Dice tend to combine low frequency words and collocation segments are short. They improve the SMT system by smoothing the translation units. And third, Gravity- Counts tends to combine high and low frequency words and collocation segments are long. However, in this case, the SMT system is not improved. Thus, the road-map for translation system improvement is to introduce new phrases with either low frequency or high frequency words. It is hard to introduce new phrases with low and high frequency words in order to improve translation quality. Experimental results are reported in the Frenchto- English IWSLT 2010 evaluation where our system was ranked 3rd out of nine systems.Postprint (published version
Nonperturbative aspects of ABJM theory
Using the matrix model which calculates the exact free energy of ABJM theory
on S^3 we study non-perturbative effects in the large N expansion of this
model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We
propose a general prescription to extract spacetime instanton actions from
general matrix models, in terms of period integrals of the spectral curve, and
we use it to determine them explicitly in the ABJM matrix model, as exact
functions of the 't Hooft coupling. We confirm numerically that these
instantons control the asymptotic growth of the genus expansion. Furthermore,
we find that the dominant instanton action at strong coupling determined in
this way exactly matches the action of an Euclidean D2-brane instanton wrapping
RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published
in JHE
Holomorphic anomaly and matrix models
The genus g free energies of matrix models can be promoted to modular
invariant, non-holomorphic amplitudes which only depend on the geometry of the
classical spectral curve. We show that these non-holomorphic amplitudes satisfy
the holomorphic anomaly equations of Bershadsky, Cecotti, Ooguri and Vafa. We
derive as well holomorphic anomaly equations for the open string sector. These
results provide evidence at all genera for the Dijkgraaf--Vafa conjecture
relating matrix models to type B topological strings on certain local
Calabi--Yau threefolds.Comment: 23 pages, LaTex, 3 figure
PT-symmetric interpretation of double-scaling
The conventional double-scaling limit of an O(N)-symmetric quartic quantum
field theory is inconsistent because the critical coupling constant is
negative. Thus, at the critical coupling the Lagrangian defines a quantum
theory with an upside-down potential whose energy appears to be unbounded
below. Worse yet, the integral representation of the partition function of the
theory does not exist. It is shown that one can avoid these difficulties if one
replaces the original theory by its PT-symmetric analog. For a zero-dimensional
O(N)-symmetric quartic vector model the partition function of the PT-symmetric
analog is calculated explicitly in the double-scaling limit.Comment: 11 pages, 2 figure
Interacting fermions and N=2 Chern-Simons-matter theories
The partition function on the three-sphere of N=3 Chern-Simons-matter
theories can be formulated in terms of an ideal Fermi gas. In this paper we
show that, in theories with N=2 supersymmetry, the partition function
corresponds to a gas of interacting fermions in one dimension. The large N
limit is the thermodynamic limit of the gas and it can be analyzed with the
Hartree and Thomas-Fermi approximations, which lead to the known large N
solutions of these models. We use this interacting fermion picture to analyze
in detail N=2 theories with one single node. In the case of theories with no
long-range forces we incorporate exchange effects and argue that the partition
function is given by an Airy function, as in N=3 theories. For the theory with
g adjoint superfields and long-range forces, the Thomas-Fermi approximation
leads to an integral equation which determines the large N, strongly coupled
R-charge.Comment: 29 pages, 4 figure
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