Narrow Results

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.

A string in four dimensions is constructed by supplementing it with 44 Majorana fermions. The later are represented by 11 vectors in the bosonic representation SO(D-1,1). The central charge is 26. The fermions are grouped in such a way that the resulting action is worldsheet supersymmetric. The energy–momentum and current generators satisfy the super-Virasoro algebra. GSO projections are necessary for proving modular invariance. Space–time supersymmetry algebra is deduced and is substantiated for specific modes of zero mass. The symmetry group of the model can descend to the low energy standard model group SU(3)×SU_L(2)×U_Y(1) through the Pati–Salam group.

A derivation of N = 1 supergravity action from string theory is presented. Starting from a Nambu–Goto bosonic string, matter field is introduced to obtain a superstring in four dimensions. The excitation quanta of this string contain graviton and the gravitino. Using the principle of equivalence, the action in curved space–time are found and the sum of them is the Deser–Zumino N = 1 supergravity action. The energy tensor is Lorentz invariant due to supersymmetry.

A four-dimensional superstring have been constructed starting from a 26-dimensional bosonic string. Fermions are introduced by noting the Mandelstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO(6) ⊗ SO(5) in the worldsheet. It has four bosonic coordinates and 44 Majorana fermions of SO(3, 1). Here the superstring action is shown to be invariant under conformal and superconformal transformations with the usual conformal and superconformal ghosts of the ten-dimensional superstrings. The massless spectrum obtained by quantizing the action, contain vector mesons which are generators of the SO(6) ⊗ SO(5). Using Wilson loops, this product group is proven to descend to Z₃ ⊗ SU(3) ⊗ SU(2) ⊗ U(1) without breaking supersymmetry. Thus there are just three generations of quarks and leptons.

We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional supersymmetric SU(N) Yang–Mills on ℝ⁴ × S¹ and as Kähler gravity on local SU(N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU(N) Seiberg–Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of S¹ can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang–Mills is the low temperature limit of the statistical model, where the statistical model is frozen to a ground state that is associated with the local SU(N) geometry. We also show that the low temperature limit corresponds to a certain degeneration of amoebas and the Ronkin functions known as tropical geometry.

Recently we considered supertwistor reformulation of the D = 4, N = 1, 2 superstring action that comprises Newman–Penrose dyad components and is classically equivalent to the Green–Schwarz one. It was shown that in the covariant κ-symmetry gauge the supertwistor representation of the string action is simplified. Here, we analyze its Hamiltonian formulation, classify the constraints on the phase-space variables, and find the covariant set of generators of the gauge symmetries. Quantum symmetries of the supertwistor representation of the string action are examined by applying the worldsheet CFT technique. Considered are various generalizations of the model from the perspective of their possible relation to the known twistor superstring models.

In the present paper we develop a concept of parallel ordinary (O) and mirror (M) worlds. We have shown that in the case of a broken mirror parity (MP), the evolutions of fine structure constants in the O- and M-worlds are not identical. It is assumed that E₆-unification inspired by superstring theory restores the broken MP at the scale ~ 10¹⁸GeV, what unavoidably leads to the different E₆-breakdowns at this scale: E₆ → SO(10) × U(1)_Z — in the O-world, and E′₆ → SU(6)′ × SU(2)′_Z — in the M-world. Considering only asymptotically free theories, we have presented the running of all the inverse gauge constants in the one-loop approximation. Then a "quintessence" scenario suggested in Refs. 56–61 is discussed for our model of accelerating universe. Such a scenario is related with an axion ("acceleron") of a new gauge group SU(2)′_Z which has a coupling constant g_Z extremely growing at the scale Λ_Z ~ 10^-3eV.

We perform a direct test of the gauge/gravity duality by studying one-dimensional U(N) gauge theory with 16 supercharges at finite temperature using Monte Carlo simulation. In the 't Hooft large-N limit and in the strong coupling limit, the model is expected to have a dual gravity description in terms of the near-extremal black 0-brane solution in ten-dimensional type IIA supergravity. Our results provide the first example, in which the microscopic origin of the black hole thermodynamics is accounted for by solving explicitly the strongly coupled dynamics of the open strings attached to the D-branes.

We improve relation between type IIB and type I superstring theory. In fact we obtain type I theory as type IIB on the solution of appropriately chosen boundary conditions. We find that type I theory, which is symmetric under world-sheet parity transformation Ω : σ → - σ, beside Ω even fields of the type IIB theory, contains squares of Ω odd fields.

The 26-dimensional bosonic string, first suggested by Nambu and Goto, is reduced to a four-dimensional superstring by using two species of six and five Majorana fermions as proposed by Deo. These two species of fermions differ in their "neutrino-like" phase, and are vectors in the bosonic representation SO(d-1, 1). Using Polchinski's equivalence between operators and states, we can write the Virasoro generators for four-dimensional string theory. The theory is shown to give the same results as given by other superstrings and also reveals the well-known aspects of four-dimensional string theory. The bosons and the fermions are found to be the basis for constructing this string theory which includes gravity and exhibits strong–weak coupling duality as well as the usual electric–magnetic duality. This formalism is used to calculate the metric tensor as well as the entropy–area relation for a black hole.

The first lecture gives a colloquium-level overview of string theory and M-theory. The second lecture surveys various attempts to construct a viable model of particle physics. A recently proposed approach, based on F-theory, is emphasized.

More than one third of the 88 globally-independent Cellular Automata rules exhibit robust simple Bernoulli-shift dynamics. Among them we find rule , which we proved to be chaotic in the previous episodes of our chronicle, and rule , the famous global majority rule. Therefore, we cannot overstate the importance of the Bernoulli σ_τ-shift rules which we will present in two parts of our continuing odyssey on the Nonlinear Dynamics Perspective of Cellular Automata. This paper covers the first 15 of the 30 Bernoulli σ_τ-shift rules. In this paper, after recalling the main concepts of Bernoulli rules — such as the role of the three Bernoulli parameters σ, τ and β — we will display the basin tree diagrams of these rules together with a convenient summary of the results extracted from them. Then, we will show that the superstring is an excellent testing signal to find the robust behavior of a given rule. Finally, we will conclude this paper with a discussion about the difference between robust and nonrobust ω-limit orbits of the Bernoulli σ_τ-shift rules.

Over the past eight years, we have studied one of the simplest, yet extremely interesting, dynamical systems; namely, the one-dimensional binary Cellular Automata. The most remarkable results have been presented in a series of papers which is concluded by the present article. The final stop of our odyssey is devoted to the analysis of the second half of the 30 Bernoulli σ_τ-shift rules, which constitute the largest among the six groups in which we classified the 256 local rules. For all these 15 rules, we present the basin-tree diagrams obtained by using each bit string with L ≤ 8 as initial state, a summary of the characteristics of their ω-limit orbits, and the space-time patterns generated from the superstring. Also, in the last section we summarize the main results we obtained by means of our "nonlinear dynamics perspective".

The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring) ${ℳ}$, we classify analogs of Bol operators invariant under the simple maximal subalgebra $𝔥$ of the same rank as its simple ambient superalgebra $𝔤$ of vector fields on ${ℳ}$ and containing all elements of negative degree of $𝔤$ in a $\mathbb{Z}$-grading. We also consider the Lie superalgebras of vector fields $𝔤$ preserving a contact structure on the superstring ${ℳ}$. We have discovered many new operators.

String theory/M-theory general predicts that axionic fields with a broad mass spectrum extending below 10^-10eV are produced after compactification to four dimensions. These axions/fields provoke a rich variety of cosmophysical phenomena on different scales depending on their masses and provide us new windows to probe the ultimate theory. In this article, after overviewing this axiverse idea¹, I take up the black hole instability as the most fascinating one among such axionic phenomena and explain its physical mechanism and astrophysical predictions.

More than one third of the 88 globally-independent Cellular Automata rules exhibit robust simple Bernoulli-shift dynamics. Among them we find rule 170 , which we proved to be chaotic in the previous episodes of our chronicle, and rule 184 , the famous global majority rule. Therefore, we cannot overstate the importance of the Bernoulli σ_τ-shift rules which we will present in two parts of our continuing odyssey on the Nonlinear Dynamics Perspective of Cellular Automata. This paper covers the first 15 of the 30 Bernoulli σ_τ-shift rules. In this paper, after recalling the main concepts of Bernoulli rules — such as the role of the three Bernoulli parameters σ, τ and β — we will display the basin tree diagrams of these rules together with a convenient summary of the results extracted from them. Then, we will show that the superstring is an excellent testing signal to find the robust behavior of a given rule. Finally, we will conclude this paper with a discussion about the difference between robust and nonrobust ω-limit orbits of the Bernoulli σ_τ-shift rules.

Over the past eight years, we have studied one of the simplest, yet extremely interesting, dynamical systems; namely, the one-dimensional binary Cellular Automata. The most remarkable results have been presented in a series of papers which is concluded by the present article. The final stop of our odyssey is devoted to the analysis of the second half of the 30 Bernoulli σ_τ-shift rules, which constitute the largest among the six groups in which we classified the 256 local rules. For all these 15 rules, we present the basin-tree diagrams obtained by using each bit string with L ≤ 8 as initial state, a summary of the characteristics of their ω-limit orbits, and the space-time patterns generated from the superstring. Also, in the last section we summarize the main results we obtained by means of our “nonlinear dynamics perspective”.