اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدElliptic Selberg integrals and conformal blocks
69
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present an elliptic version of Selbergs integral formula.
قيم البحث
اقرأ أيضاً
In the previous paper (J. Combin. Theory Ser. A, 120, 2013, 1263--1284) H. Tagawa and the two authors proposed an algebraic method to compute certain Pfaffians whose form resemble to Hankel determinants associated with moment sequences of the classic
al orthogonal polynomials. At the end of the paper they offered several conjectures. In this work we employ a completely different method to evaluate this type of Pfaffians. The idea is to apply certain de Bruijn type formula and convert the evaluation of the Pfaffians to the certain Selberg type integrals. This approach works not only for Pfaffians but also for hyperpfaffians. Hence it enables us to establish much more generalized identities than those conjectured in the previous paper. We also attempt q-analogues.
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding spa
ce formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.
We give a simple iterative procedure to compute the classical conformal blocks on the sphere to all order in the modulus.
We show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bundles of conformal blocks have rank one, this construction may be comp
ared with the old integral formulas of the second and the third author. The proportionality coefficients are some Selberg type integrals which are computed. Finally, a geometric construction of the tensor products of vector representations of the Lie algebra $frak{gl}(m)$ is proposed.
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks in three dimensions.
Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
