Related papers: On Nonlinear Superconformal Algebras With N > 4
At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of strongly nonlinear field can form a non-associative algebra. It is shown that such algebra can be described as an algebra of…
In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…
We consider the sl(2) current algebra at level k=-4 when the sl(2) BRST operator is nilpotent. We formulate a spectral sequence converging to the cohomology of this BRST operator. At the second term of the spectral sequence, we observe an…
We study the $N=2$ string with a real structure on the $(2,2)$ spacetime, using BRST methods. Several new features emerge. In the diagonal basis, the operator $\exp(\lambda \int^z J^{\rm tot})$, which is associated with the moduli for the…
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear,…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
We present simple first-class-constraint actions and BRST operators for the 4D N=4 superparticle. Each generation of ghosts has 2 super-indices, like the coordinates. The constraints that define projective superspace close in a super…
The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second…
General structure of BRST-invariant constraint algebra is established, in its commutator and antibracket forms, by means of formulation of algebra-generating equations in yet more extended phase space. New ghost-type variables behave as…
The $\cal{N}=4$ supersymmetric spinning particle admits several consistent quantizations, related to the gauging of different subgroups of the $SO(4)$ $R$-symmetry on the worldline. We construct the background independent BRST quantization…
In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both $d=4$ and $d=3$. For the super-Carrollian algebra in $d=4$, we identify multiple admissible structures,…
We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson…
We show that with every classical system possessing first class constraints that form a natural Lie algebra, we can associate a superalgebra that admits the constraint Lie algebra as a subalgebra. An odd generator of this superalgebra that…
We write the BRST operator of the N=2 superstring as $Q= e^{-R} (\oint \frac{dz}{2\pi i} ~ b \gamma_+ \gamma_-)e^R$ where $b$ and $gamma_\pm$ are super-reparameterization ghosts. This provides a trivial proof of the nilpotence of this…
This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…
Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie (super)algebras admit ``quantum''…
In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with $N\!-\!2$…
We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…
The action for classical and consequently quantum N=1, D=4, supersymmetric Yang-Mills theories is proven to be written as a BRST exact term. In order to show this, the space of fields in the theory must be enlarged to include an extrafield…