ترغب بنشر مسار تعليمي؟ اضغط هنا

Code conformal field theory and framed algebra

333   0   0.0 ( 0 )
 نشر من قبل Yuto Moriwaki
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Yuto Moriwaki




اسأل ChatGPT حول البحث

It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we introduce a notion of a framed algebra, which is a finite-dimensional non-associative algebra, and showed that the category of framed algebras and the category of code conformal field theories are equivalent. We have also constructed a new family of integrable conformal field theories using this equivalence. These conformal field theories are expected to be useful for the study of moduli spaces of conformal field theories.



قيم البحث

اقرأ أيضاً

133 - J. Fuchs , C. Schweigert 2000
The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures one encoun ters also appear in other areas of physics and mathematics. In particular, they lead to two conjectures on the sub-bundle structure of chiral blocks, and they are instrumental in the study of conformally invariant boundary conditions.
219 - Chongying Dong , Xingjun Lin , 2012
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of any rational , C_2-cofinite vertex operator algebra is a congruence subgroup. In particular, the q-character of each irreducible module is a modular function on the same congruence subgroup. The Galois symmetry of the modular representations is obtained and the order of the anomaly for those modular categories satisfying some integrality conditions is determined.
The idea of summing over all intermediate states that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal vertex algebras , one deals with coends in functor categories. Working with these coends involves quite a few subtleties which, even though they have in principle already been understood twenty years ago, have not been sufficiently appreciated by the conformal field theory community.
Given formal differential operators $F_i$ on polynomial algebra in several variables $x_1,...,x_n$, we discuss finding expressions $K_l$ determined by the equation $exp(sum_i x_i F_i)(exp(sum_j q_j x_j)) = exp(sum_l K_l x_l)$ and their applications. The expressions for $K_l$ are related to the coproducts for deformed momenta for the noncommutative space-times of Lie algebra type and also appear in the computations with a class of star products. We find combinatorial recursions and derive formal differential equations for finding $K_l$. We elaborate an example for a Lie algebra $su(2)$, related to a quantum gravity application from the literature.
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^infty(M) otimes M(3,C), where M is a space-time manifo ld. This calculus is covariant under the action and coaction of finite dimensional dual quantum groups. We study the star structures on these quantum groups and the compatible one in M(3,C). This leads to an invariant scalar product on the later space. We analyse the differential algebra Omega(M(3,C)) in terms of quantum group representations, and consider in particular the space of one-forms on S since its elements can be considered as generalized gauge fields.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا