13,029 research outputs found
Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I
Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional
physical theory (a compactification of ``M-theory'') and a four-dimensional
physical theory (using the ``F-theory'' construction). A key issue in both
theories is the calculation of the ``superpotential''of the theory. We propose
a systematic approach to identify these divisors, and derive some criteria to
determine whether a given divisor indeed contributes. We then apply our
techniques in explicit examples, in particular, when the base B of the elliptic
fibration is a toric variety or a Fano 3-fold. When B is Fano, we show how
divisors contributing to the superpotential are always "exceptional" (in some
sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions
of X, that is birational transformations to a singular model (where the image
of D no longer contributes) as well as certain smoothings of the singular
model. If a smoothing exists, then the Hodge numbers change. We speculate that
divisors contributing to the superpotential are always "exceptional" (in some
sense) for X, also in M-theory. In fact we show that this is a consequence of
the (log)-minimal model algorithm in dimension 4, which is still conjectural in
its generality, but it has been worked out in various cases, among which toric
varieties.Comment: Reference added; 34 pages with 7 figures AmS-TeX version 2.
Aspects of Quantum Fermionic T-duality
We study two aspects of fermionic T-duality: the duality in purely fermionic
sigma models exploring the possible obstructions and the extension of the
T-duality beyond classical approximation. We consider fermionic sigma models as
coset models of supergroups divided by their maximally bosonic subgroup
OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional
gauge fixing we derive their fermionic T-duals. In the second part of the
paper, we prove the conformal invariance of these models at one and two loops
using the Background Field Method and we check the Ward Identities.Comment: 65 pages, 5 figure
The Background Field Method and the Linearization Problem for Poisson Manifolds
The background field method (BFM) for the Poisson Sigma Model (PSM) is
studied as an example of the application of the BFM technique to open gauge
algebras. The relationship with Seiberg-Witten maps arising in non-commutative
gauge theories is clarified. It is shown that the implementation of the BFM for
the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a
generalized linearization problem (in the formal sense) for Poisson structures
in the presence of gauge fields. Sufficient conditions for the existence of a
solution and a constructive method to derive it are presented.Comment: 33 pp. LaTex, references and comments adde
Non-Critical Covariant Superstrings
We construct a covariant description of non-critical superstrings in even
dimensions. We construct explicitly supersymmetric hybrid type variables in a
linear dilaton background, and study an underlying N=2 twisted superconformal
algebra structure. We find similarities between non-critical superstrings in
2n+2 dimensions and critical superstrings compactified on CY_(4-n) manifolds.
We study the spectrum of the non-critical strings, and in particular the
Ramond-Ramond massless fields. We use the supersymmetric variables to construct
the non-critical superstrings sigma-model action in curved target space
backgrounds with coupling to the Ramond-Ramond fields. We consider as an
example non-critical type IIA strings on AdS_2 background with Ramond-Ramond
2-form flux.Comment: harvmac, amssym, 46 p
Curved Beta-Gamma Systems and Quantum Koszul Resolution
We consider the partition function of beta-gamma systems in curved space of
the type discussed by Nekrasov and Witten. We show how the Koszul resolution
theorem can be applied to the computation of the partition functions and to
characters of these systems and find a prescription to enforce the hypotheses
of the theorem at the path integral level. We illustrate the technique in a few
examples: a simple 2-dimensional target space, the N-dimensional conifold, and
a superconifold. Our method can also be applied to the Pure Spinor constraints
of superstrings.Comment: harvmac, 17 page
Super-Chern-Simons Theory as Superstring Theory
Superstrings and topological strings with supermanifolds as target space play
a central role in the recent developments in string theory. Nevertheless the
rules for higher-genus computations are still unclear or guessed in analogy
with bosonic and fermionic strings. Here we present a common geometrical
setting to develop systematically the prescription for amplitude computations.
The geometrical origin of these difficulties is the theory of integration of
superforms. We provide a translation between the theory of supermanifolds and
topological strings with supertarget space. We show how in this formulation one
can naturally construct picture changing operators to be inserted in the
correlation functions to soak up the zero modes of commuting ghost and we
derive the amplitude prescriptions from the coupling with an extended
topological gravity on the worldsheet. As an application we consider a simple
model on R^(3|2) leading to super-Chern-Simons theory.Comment: hravmac, 50p
Super Background Field Method for N=2 SYM
The implementation of the Background Field Method (BFM) for quantum field
theories is analysed within the Batalin-Vilkovisky (BV) formalism. We provide a
systematic way of constructing general splittings of the fields into classical
and quantum parts, such that the background transformations of the quantum
fields are linear in the quantum variables. This leads to linear Ward-Takahashi
identities for the background invariance and to great simplifications in
multiloop computations. In addition, the gauge fixing is obtained by means of
(anti)canonical transformations generated by the gauge-fixing fermion. Within
this framework we derive the BFM for the N=2 Super-Yang-Mills theory in the
Wess-Zumino gauge viewed as the twisted version of Donaldson-Witten topological
gauge theory. We obtain the background transformations for the full BRST
differential of N=2 Super-Yang-Mills (including gauge transformations, SUSY
transformations and translations). The BFM permits all observables of the
supersymmetric theory to be identified easily by computing the equivariant
cohomology of the topological theory. These results should be regarded as a
step towards the construction of a super BFM for the Minimal Supersymmetric
Standard Model.Comment: 34 pages, Latex, JHEP3.cl
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