Related papers: ON THE EXTENDED POINCARE POLYNOMIAL

We present several examples of T^8/P orbifolds with $P \subset SU(4)$. We compute their Hodge numbers and consider turning on discrete torsion. We then study supersymmetric compactifications of type II, heterotic, and type I strings on…

We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson…

We propose some general growth conditions on the function $% f=f\left( x,\xi \right) $, including the so-called natural growth, or polynomial, or $p,q-$growth conditions, or even exponential growth, in order to obtain that any local…

The Wigner-Eckart theorem is a well known result for tensor operators of su(2) and, more generally, any compact Lie algebra. In this paper the theorem will be generalized to the particular non-compact case of sl(2,R). In order to do so,…

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory,…

We study ${\cal N}=2$ compactifications of heterotic string theory on the CHL orbifold $(K3\times T^2)/\mathbb{Z}_N$ with $N= 2, 3, 5, 7$. $\mathbb{Z}_N$ acts as an involution on $K3$ together with a shift of $1/N$ along one of the circles…

By identifying the moduli space of coupling constants in the SYM description of toroidal compactifications of M(atrix)-Theory, we construct the M(atrix) description of the moduli spaces of Type IIA string theory compactified on T^n.…

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…

In this note we introduce a new class of refined Eulerian polynomials defined by $$A_n(p,q)=\sum_{\pi\in\mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)},$$ where ${\rm odes}(\pi)$ and ${\rm edes}(\pi)$ enumerate the number of descents…

Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order…

We consider Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d dimensions. We give an explicit construction of the field theory description of this system by putting a countably infinite…

We construct the effective action for toroidal compactifications of bosonic string theory from generalized Scherk-Schwarz reductions of double field theory. The enhanced gauge symmetry arising at special points in moduli space is…

We analyse the spectrum of the D-dimensional Poincare invariant effective string model of Polchinski and Strominger. It is shown that the leading terms beyond the Casimir term in the long distance expansion of the spectrum have a universal…

We define a new elliptic genus psi on the complex bordism ring. With coefficients in Z[1/2], we prove that it induces an isomorphism of the complex bordism ring modulo the ideal which is generated by all differences P(E)-P(E*) of projective…

We have shown that two of the most studied models of lineal gravities - Liouville gravity and a ``string-inspired'' model exhibiting the main characteristic features of a black-hole solution - can be formulated as gauge invariant theories…

We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…

Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They computed these two partial-dual genus polynomials of four families of ribbon graphs, posed some research…

Let $\pi, \pi'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincar\'e pairing $EP (\pi,\pi')$, the alternating sum of the dimensions of the Ext-groups. We show that $EP (\pi,\pi')$…

We study compactifications of the heterotic pure spinor superstring to six and four dimensions focusing on two simple Calabi-Yau orbifolds. We show that the correct spectrum can be reproduced only if, in the twisted sector, there remain…