اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDeformations of special geometry: in search of the topological string
142
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus $gleq3$ contributions are constructed explicitly for a general class of effective actions associated with a special-Kahler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.
قيم البحث
اقرأ أيضاً
It is shown that the generating function of $mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT
, realises in string theory the six-dimensional $varOmega$-background of Nekrasov, in the case of opposite deformation parameters $epsilon_1=-epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $mathscr{N}=2$ and $mathscr{N}=2^*$ theories.
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straig
htforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of $SL(2,{mathbb Z})$) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of an hyperbolic three-geometry associated with $q$-series in the computation of the string amplitudes.
A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw-Teitelboim gravity wi
th a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large $p$ limit of a natural deformation of the $(2,p)$ minimal string theory.
The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry, related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of spe
cial geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.
We study the attractor equations for a quantum corrected prepotential F=t^3+ilambda, with lambda in R,which is the only correction which preserves the axion shift symmetry and modifies the geometry. By performing computations in the ``magnetic char
ge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). For a certain range of the quantum parameter lambda we find a ``separation of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. Furthermore, we find that, away from the classical limit, a ``transmutation of the supersymmetry-preserving features of the attractors takes place when lambda reaches a particular critical value.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
