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  • articleNo Access

    QUANTUM STATE DENSITY AND CRITICAL TEMPERATURE IN M-THEORY

    We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature TH. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology formula. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

  • articleNo Access

    FREE FIELD EQUATIONS FOR SPACE–TIME ALGEBRAS WITH TENSORIAL MOMENTUM

    Free field equations, with various spins, for space–time algebras with second-rank tensor (instead of the usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. Special attention is paid to gauge invariance properties, in particular the spin-two equations with gauge invariance are constructed for dimensions 2+2 and 2+4, and the connection with Einstein equation and diffeomorphism invariance is established.

  • articleNo Access

    PENROSE LIMIT OF AdS4 × N0,1,0 AND formula GAUGE THEORY

    We consider M-theory on AdS4 × N0,1,0 where N0,1,0 = (SU(3) × (2))/(SU(2) × U(1)). We review a Penrose limit of AdS4 × N0,1,0 that provides the pp-wave geometry of AdS4 × S7. There exists a subsector of three-dimensional formula dual gauge theory, by taking both the conformal dimension and R-charge large with the finiteness of their difference, which has enhanced formula maximal supersymmetry. We identify operators in the formula gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the formula gauge theory operators originating from both formula short vector multiplet and formula long gravitino multiplet fall into formula supermultiplets.

  • articleNo Access

    LITTLE GROUPS OF PREON BRANES

    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 Td-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.

  • articleNo Access

    Adventures in Eleven Dimensions

    In ten dimensions, SO(8) triality encourages confusion between fermions ans bosons, but in eleven dimensions, SO(9) has no such features. Yet this is the domain of M — theory whose infrared limit is the divergent supergravity field theory. Curtright ascribes this divergence to an incomplete cancellation among the Dynkin indices between the supergravity representations. We speculate that an infinite number of the recently discovered Euler triplets, describing massless particles of higher spin, can cancel the divergences of eleven dimensional supergravity, perhaps providing a clue to M — theory.

  • articleNo Access

    10D N=1 MASSLESS BPS SUPERMULTIPLETS

    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(kn), with k1+⋯+kn=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.

  • articleNo Access

    ARGUMENTS FOR F-THEORY

    After a brief review of string and M-theory we point out some deficiencies. Partly to rectify them, we present several arguments for "F-theory", enlarging spacetime to (2, 10) signature, following the original suggestion of C. Vafa. We introduce a suggestive supersymmetric 27-plet of particles, associated to the exceptional symmetric hermitian space E6/Spinc(10). Several possible future directions, including using projective rather than metric geometry, are mentioned. We should emphasize that F-theory is yet just a very provisional attempt, lacking clear dynamical principles.

  • articleNo Access

    REMARKS ON E11 APPROACH

    We consider a few topics in E11 approach to superstrings/M-theory: even subgroups (Z2 orbifolds) of En, 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.

  • articleNo Access

    NEW TWO-DIMENSIONAL MASSLESS FIELD THEORY FROM BAGGER–LAMBERT–GUSTAVSSON MODEL

    By compactifying the Bagger–Lambert–Gustavsson model on ℝ1,1×S1, we obtain a new two-dimensional massless field theory with dynamical fields valued in the Lie three-algebra formula coupled with an SO(1, 1) scalar and vector field which are valued in the set formula of the endomorphisms of the Lie three-algebra. In the limit gBLG→∞ the theory reduces to a supersymmetric Lie three-valued generalization of the Green–Schwarz superstring in the light-cone gauge.

  • articleNo Access

    EXACT ABJM PARTITION FUNCTION FROM TBA

    We report on the exact computation of the S3 partition function of U(N)k × U(N)-k ABJM theory for k = 1, N = 1, …, 19. The result is a polynomial in π-1 with rational coefficients. As an application of our results, we numerically determine the coefficient of the membrane 1-instanton correction to the partition function.

  • articleNo Access

    A class of Hermitian generalized Jordan triple systems and Chern–Simons gauge theory

    We find a class of Hermitian generalized Jordan triple systems (HGJTSs) and Hermitian (ϵ, δ)-Freudenthal–Kantor triple systems (HFKTSs). We apply one of the most simple HGJTSs which we find to a field theory and obtain a typical u(N) Chern–Simons gauge theory with a fundamental matter.

  • articleNo Access

    The birth of the universe in a new G-theory approach

    Recently, Padmanabhan has discussed that the expansion of the cosmic space is due to the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region. Now, a natural question arises that how these degrees of freedom emerged from nothing? We try to address this issue in a new theory which is more complete than M-theory and reduces to it with some limitations. In M-theory, there is no stable object like stable M3-branes that our universe is formed on it and for this reason cannot help us to explain cosmological events. In this research, we propose a new theory, named G-theory which could be the mother of M-theory and superstring theory. In G-theory, at the beginning, two types of G0-branes, one with positive energy and one with negative energy are produced from nothing in 14 dimensions. Then, these branes are compactified on three circles via two different ways (symmetrically and anti-symmetrically), and two bosonic and fermionic parts of action for M0-branes are produced. By joining M0-branes, supersymmetric Mp-branes are created which contain the equal number of degrees of freedom for fermions and bosons. Our universe is constructed on one of Mp-branes and other Mp-brane and extra energy play the role of bulk. By dissolving extra energy which is produced by compacting actions of Gp-branes, into our universe, the number of degrees of freedom on it and also its scale factor increase and universe expands. We test G-theory with observations and find that the magnitude of the slow-roll parameters and the tensor-to-scalar ratio in this model are very much smaller than one which are in agreement with predictions of experimental data. Finally, we consider the origin of the extended theories of gravity in G-theory and show that these theories could be anomaly free.

  • articleNo Access

    G-theory: The generator of M-theory and supersymmetry

    In string theory with ten dimensions, all Dp-branes are constructed from D0-branes whose action has two-dimensional brackets of Lie 2-algebra. Also, in M-theory, with 11 dimensions, all Mp-branes are built from M0-branes whose action contains three-dimensional brackets of Lie 3-algebra. In these theories, the reason for difference between bosons and fermions is unclear and especially in M-theory there is not any stable object like stable M3-branes on which our universe would be formed on it and for this reason it cannot help us to explain cosmological events. For this reason, we construct G-theory with M dimensions whose branes are formed from G0-branes with N-dimensional brackets. In this theory, we assume that at the beginning there is nothing. Then, two energies, which differ in their signs only, emerge and produce 2M degrees of freedom. Each two degrees of freedom create a new dimension and then M dimensions emerge. M-N of these degrees of freedom are removed by symmetrically compacting half of M-N dimensions to produce Lie-N-algebra. In fact, each dimension produces a degree of freedom. Consequently, by compacting M-N dimensions from M dimensions, N dimensions and N degrees of freedom is emerged. These N degrees of freedoms produce Lie-N-algebra. During this compactification, some dimensions take extra i and are different from other dimensions, which are known as time coordinates. By this compactification, two types of branes, Gp and anti-Gp-branes, are produced and rank of tensor fields which live on them changes from zero to dimension of brane. The number of time coordinates, which are produced by negative energy in anti-Gp-branes, is more sensible to number of times in Gp-branes. These branes are compactified anti-symmetrically and then fermionic superpartners of bosonic fields emerge and supersymmetry is born. Some of gauge fields play the role of graviton and gravitino and produce the supergravity. The question may arise that what is the physical reason which shows that this theory is true. We shown that G-theory can be reduced to other theories like nonlinear gravity theories in four dimensions. Also, this theory, can explain the physical properties of fermions and bosons. On the other hand, this theory explains the origin of supersymmetry. For this reason, we can prove that this theory is true. By reducing the dimension of algebra to three and dimension of world to 11 and dimension of brane to four, G-theory is reduced to F(R)-gravity.

  • articleNo Access

    On the Octonionic Superconformal M-Algebra

    It is shown that besides the standard real algebraic framework for M-theory a consistent octonionic realization can be introduced. The octonionic M-superalgebra and superconformal M-algebra are derived. The first one involves 52 real bosonic generators and presents a novel and surprising feature, its octonionic M5 (super-5-brane) sector coincides with the M1 and M2 sectors. The octonionic superconformal M-algebra is given by OSp(1,8∣O) and admits 239 bosonic and 64 fermionic generators.

  • articleNo Access

    Twisted Sectors and Chern–Simons Terms in M-Theory Orbifolds

    It is shown that the twisted sector spectrum, as well as the associated Chern–Simons interactions, can be determined on M-theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes arising within the context of an explicit R6 × S1/Z2 × T4/Z2 orbifold, although the results are completely general. Local anomaly cancellation in this context is shown to require fractional anomaly data that can only arise from a twisted sector on the seven-planes, thus determining the twisted spectrum up to a small ambiguity. These results open the door to the construction of arbitrary M-theory orbifolds, including those containing fixed four-planes which are of phenomenological interest.

  • articleNo Access

    An M-Theory Perspective on Heterotic K3 Orbifold Compactifications

    We analyze the structure of heterotic M-theory on K3 orbifolds by presenting a comprehensive sequence of M-theoretic models constructed on the basis of local anomaly cancellation. This is facilitated by extending the technology developed in our previous papers to allow one to determine "twisted" sector states in nonprime orbifolds. These methods should naturally generalize to four-dimensional models, which are of potential phenomenological interest.

  • articleNo Access

    SUPERPOTENTIAL OF THE M-THEORY CONIFOLD AND TYPE IIA STRING THEORY

    The membrane instanton superpotential for M-theory on the G2 holonomy manifold given by the cone on S3×S3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

  • articleNo Access

    STRING THEORY AND THE FUZZY TORUS

    We outline a brief description of noncommutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.

  • articleNo Access

    ON EFFECTIVE F-THEORY ACTION IN TYPE IIA COMPACTIFICATIONS

    Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of space–time vanishes, we also prove a version of the Kriz–Sati conjecture by extending the arguments of Diaconescu–Moore–Witten. We also briefly discuss why even this special case allows interesting examples.

  • articleNo Access

    TIME AND M-THEORY

    We review our recent proposal for a background-independent formulation of a holographic theory of quantum gravity. The present paper incorporates the necessary background material on geometry of canonical quantum theory, holography and space–time thermodynamics, Matrix theory, as well as our specific proposal for a dynamical theory of geometric quantum mechanics, as applied to Matrix theory. At the heart of this review is a new analysis of the conceptual problem of time and the closely related and phenomenologically relevant problem of vacuum energy in quantum gravity. We also present a discussion of some observational implications of this new viewpoint on the problem of vacuum energy.