Narrow Results

It is shown how a noncommutative spacetime leads to an area, mass and entropy quantization condition which allows to derive the Schwarzschild black hole entropy $\frac{A}{4G}$, the logarithmic corrections, and further corrections, from the discrete mass transitions taking place among different mass states in $D=4$. The higher-dimensional generalization of the results in $D=4$ follows. The discretization of the entropy-mass relation $S=S(M)$ leads to an entropy quantization of the form $S=S(M_n)=n$, such that one may always assign $n$ “bits” to the discrete entropy, and in doing so, make contact with quantum information. The physical applications of mass quantization, like the counting of states contributing to the black hole entropy, black hole evaporation, and the direct connection to the black holes-string correspondence [G. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev. D55 (1997) 6189.] via the asymptotic behavior of the number of partitions of integers, follows. To conclude, it is shown how the recent large $N$ Matrix model (fuzzy sphere) of C.-S. Chu [A matrix model proposal for QG and the QM of black holes, preprint, arXiv:2406.01466] leads to very similar results for the black hole entropy as the physical model described in this work which is based on the discrete mass transitions originating from the noncommutativity of the spacetime coordinates.

Computing approximate patterns in strings or sequences has important applications in DNA sequence analysis, data compression, musical text analysis, and so on. In this paper, we introduce approximate k-covers and study them under various commonly used distance measures. We propose the following problem: "Given a string x of length n, a set U of m strings of length k, and a distance measure, compute the minimum number t such that U is a set of approximate k-covers for x with distance t". To solve this problem, we present three algorithms with time complexity O(km(n - k)), O(mn²) and O(mn²) under Hamming, Levenshtein and edit distance, respectively. A World Wide Web server interface has been established at for automated use of the programs.

The purpose of this paper is to present various algebraic views of multisets, and certain connections between the theory of multisets (with multiplicities in the semiring of positive integers) and natural computing, in particular membrane and DNA computing. We introduce a Gödel encoding of multisets, and find some results regarding this encoding together with new connections and interpretations. We also introduce the norm of a multiset and we find some relationships between multiset theory and number theory.

Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were given. In contrast to the classical period of a word, its abelian version is more flexible, factors of the word are considered the same under any internal permutation of their letters. We show two O(|y|²) algorithms for the computation of all abelian periods of a string y. The first one maps each letter to a suitable number such that each factor of the string can be identified by the unique sum of the numbers corresponding to its letters and hence abelian periods can be identified easily. The other one maps each letter to a prime number such that each factor of the string can be identified by the unique product of the numbers corresponding to its letters and so abelian periods can be identified easily. We also define weak abelian periods on strings and give an O(|y|log(|y|)) algorithm for their computation, together with some other algorithms for more basic problems.

In the first sections of this paper we give an elementary but rigorous approach to the construction of the quantum Bosonic and supersymmetric string system continuing the analysis of Dimock. This includes the construction of the DDF operators without using the vertex algebras. Next we give a rigorous proof of the equivalence between the light-cone and the covariant quantization methods. Finally, we provide a new and simple proof of the BRST quantization for these string models.

This paper presents a parallel algorithm for verifying that a string X is formed by the shuffle of two strings Y and Z. The algorithm runs in O(log²n) time with O(n²/log² n) processors on the EREW-PRAM model.

We perform Monte–Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature – gonihedric action. We study the anisotropic model when the coupling constants β_S for the space-like plaquettes and β_T for the transverse-like plaquettes are different. In the two limits β_S = 0 and β_T = 0 the system has been solved exactly and the main interest is to see what happens when we move away from these points towards the isotropic point, where we recover the original model. We find that the phase transition is of first order for β_T = β_S ≈ 0.25, while away from this point it becomes weaker and eventually turns to a crossover. The conclusion which can be drawn from this result is that the exact solution at the point β_S = 0 in terms of 2D-Ising model should be considered as a good zero-order approximation in the description of the system also at the isotropic point β_S = β_T and clearly confirms the earlier findings that at the isotropic point the original model shows a first-order phase transition.

We use Berkovits' pure spinor quantization to compute various three-point tree correlation functions in position-space for the Type IIB superstring. We solve the constraint equations for the vertex operators and obtain explicit expressions for the graviton and axion components of the vertex operators. Using these operators we compute tree level correlation functions in flat space and discuss their extension to the AdS₅ × S⁵ background.

The bosonic string propagating in AdS_D+1 is made Weyl invariant to leading and sub-leading order in large D by a ghost–matter coupling that despite modifying the target-space still preserves the Poincaré symmetry of the boundary.

We calculate the symmetry currents for type IIB superstring on a maximally supersymmetric plane wave background using the N = (2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N = (2,2) worldsheet fields. As the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.

We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p₊ and p_- are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.

Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,…,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group T_d-2 on a subgroup of (SO(d-2) × R-invariance) group. E.g. at d=9 the subgroup is exceptional G₂ group. It is also argued, that 11D Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized spacetimes with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.

A ℛ "dual" transform is introduced which relates Quantum Field Theory and String regimes, both in a curved background with D-non-compact dimensions. This operation maps the characteristic length of one regime into the other (and, as a consequence, mass domains as well). The ℛ-transform is not an assumed or a priori imposed symmetry but is revealed by the QFT and String dynamics in curved backgrounds. The Hawking–Gibbons temperature and the string maximal or critical temperature are ℛ-mapped one into the other. If back reaction of quantum matter is included, Quantum Field Theory and String phases appear, and ℛ-relations between them manifest as well. These ℛ-transformations are explicitly shown in two relevant examples: Black Hole and de Sitter spacetimes.

Using Clifford algebraic methods we describe how to generalize Maxwell theory of Electrodynamics associated with ordinary point-charges to a generalized Maxwell theory in Clifford spaces involving extended charges and p-forms of arbitrary rank. Clifford algebras contain the appropriate algebraic-geometric features to implement the principle of polydimensional transformations (branes of different dimensionality are rotated into each other) that could possibly lead to a proper formulation of string and M theory.

We consider d=10, N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T₈ subgroup of massless particles' little group T₈⋉SO(8). For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products T₈⋉SO(k₁)×⋯×SO(k_n), with k₁+⋯+k_n=8, where compact factor is embedded into SO(8) by triality map. We define actions of little groups on supercharge Q and construct corresponding supermultiplets. In some particular cases we show the existence of supermultiplets with both Fermi and Bose sectors consisting of the same representations of tensorial Poincaré. In addition, complete classification of supermultiplets (not restricted to T₈-invariant orbits) with rank-2 matrix of supersymmetry charges anticommutator, is given.

We calculate some nonperturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi–Yau threefold, near conifold singularities. We find a nontrivial deformation of the (real) 4n-dimensional hypermultiplet moduli space metric due to the infinite number of D-instantons, under the assumption of n tri-holomorphic commuting isometries of the metric, in the hyper-Kähler limit (i.e. in the absence of gravitational corrections).

The tremendous progress achieved through the study of black holes and branes suggests that their time-dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time-dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time-dependent strings/branes and possibly their interactions.

We consider a few topics in E₁₁ approach to superstrings/M-theory: even subgroups (Z₂ orbifolds) of E_n, n = 11, 10, 9 and their connection to Kac–Moody algebras, particularly to EE₁₁ subgroup of E₁₁; possible form of supersymmetry relation in E₁₁; decomposition of first fundamental representation l₁ w.r.t. the SO(10, 10) and its square-root at first few levels; particle orbit of l₁ ⋉ E₁₁. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in E₁₁.

We review the possibility that the Supersymmetric Standard Model arises from orbifold constructions of the E₈×E₈ Heterotic Superstring, and the phenomenological properties that such a model should have. In particular, trying to solve the discrepancy between the unification scale predicted by the Heterotic Superstring (≈g_GUT × 5.27 × 10¹⁷GeV) and the value deduced from LEP experiments (≈2 × 10¹⁶GeV), we will predict the presence at low energies of three families of Higgses and vector-like colour triplets. Our approach relies on the Fayet–Iliopoulos breaking, and this is also a crucial ingredient, together with having three Higgs families, to obtain in these models an interesting pattern of fermion masses and mixing angles at the renormalizable level. Namely, after the gauge breaking some physical particles appear combined with other states, and the Yukawa couplings are modified in a well-controlled way. On the other hand, dangerous flavour-changing neutral currents may appear when fermions of a given charge receive their mass through couplings with several Higgs doublets. We will address this potential problem, finding that viable scenarios can be obtained for a reasonable light Higgs spectrum.

Utilizing the gauge framework, software under development at Baylor University, we explicitly construct all layer 1 weakly coupled free fermionic heterotic string (WCFFHS) gauge models up to order 32 in four to ten large spacetime dimensions. These gauge models are well suited to large scale systematic surveys and, while they offer little phenomenologically, are useful for understanding the structure of the WCFFHS region of the string landscape. Herein, we present the gauge groups statistics for this swath of the landscape for both supersymmetric and non-supersymmetric models.