arXiv subjects

Murat Gunaydin

Publications and source records attributed to Murat Gunaydin.

65 records · Page 4Linked to original sources

arXiv1998

Unitary Supermultiplets of OSp(1/32,R) and M-theory

We review the oscillator construction of the unitary representations of noncompact groups and supergroups and study the unitary supermultiplets of OSp(1/32,R) in relation to M-theory. OSp(1/32,R) has a singleton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(1/32,R)_L X OSp(1/32,R)_R as the "minimal" generalized AdS supersymmetry algebra of M-theory corresponding to the embedding of two spinor representations of SO(10,2) in the fundamental representation of Sp(32,R). The contraction to the Poincare superalgebra with central charges proceeds via a diagonal subsupergroup OSp(1/32,R)_{L-R} which contains the common subgroup SO(10,1) of the two SO(10,2) factors. The parity invariant singleton supermultiplet of OSp(1/32,R)_L \times OSp(1/32,R)_R decomposes into an infinite set of "doubleton" supermultiplets of the diagonal OSp(1/32,R)_{L-R}. There is a unique "CPT self-conjugate" doubleton supermultiplet whose tensor product with itself yields the "massless" generalized AdS_{11} supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of 11-dimensional supergravity plus additional ones. Assuming that an AdS phase of M-theory exists we argue that the doubleton field theory must be the holographic superconformal field theory in ten dimensions that is dual to M-theory in the same sense as the duality between the N=4 super Yang-Mills in d=4 and the IIB superstring over AdS_5 X S^5.

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arXiv1998

Singletons, Doubletons and M-theory

We identify the two dimensional AdS subsupergroup $OSp(16/2,R)$ of the M-theory supergroup $OSp(1/32,R)$ which captures the dynamics of $n$ $D0$-branes in the large $n$ limit of Matrix theory. The $Sp(2,R)$ factor in the even subgroup $SO(16) \times Sp(2,R)$ of $OSp(16/2,R)$ corresponds to the AdS extension of the Poincare symmetry of the longitudinal directions. The infinite number of $D0$-branes with ever increasing and quantized values of longitudinal momenta are identified with the Fourier modes of the singleton supermultiplets of $OSp(16/2,R)$,which consist of 128 bosons and 128 fermions. The large $n$ limit of N=16 U(n) Yang-Mills quantum mechanics which describes Matrix theory is a conformally invariant N=16 singleton quantum mechanics living on the boundary of $AdS_{2}$. We also review some of the earlier results on the spectra of Kaluza-Klein supergravity theories in relation to the recent conjecture of Maldacena relating the dynamics of $n$ $Dp$-branes to certain AdS supergravity theories. We point out the remarkable parallel between the conjecture of Maldacena and the construction of the spectra of $11-d$ and type $IIB$ supergravity theories compactified over various spheres in terms of singleton or doubleton supermultiplets of corresponding AdS supergroups.

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arXiv1997

Orbits of Exceptional Groups, Duality and BPS States in String Theory

We give an invariant classification of orbits of the fundamental representations of exceptional groups $E_{7(7)}$ and $E_{6(6)}$ which classify BPS states in string and M theories toroidally compactified to d=4 and d=5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d=5 and d=4, respectively. The classification of BPS states preserving different numbers of supersymmetries is in close parallel to the classification of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 with symmetric space geometries are also classified including the exceptional N=2 theory that has $E_{7(-25)}$ and $E_{6(-26)}$ as its symmety in the respective dimensions.

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arXiv1997

Real forms of nonlinear superconformal and quasi-superconformal algebras and their unified realization

We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA's and SCA's and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization involves a dimension zero boson (dilaton), dimension one symmetry currents and dimension 1/2 free bosons for QSCA'a and dimension 1/2 free fermions for SCA's. The dimension 1/2 free bosons and fermions are associated with the quaternionic and super-quaternionic symmetric spaces of corresponding Lie groups and Lie supergroups, respectively. We conclude with a discussion of possible applications of our results.

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arXiv1997

Seven Sphere and the Exceptional Nonlinear Superconformal Algebras

The realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents are reviewed. Both the N=8 and N=7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G_2, with the central charges c=26/5 and c=5, respectively. They also have realizations over the coset spaces SO(8)XU(1)/SO(7) and SO(7)X U(1)/G_2 for some fixed values of their central charges. The coset space SO(8)/SO(7) is the seven-sphere , whereas the space SO(7)/G_2 represents the seven-sphere with torsion. We conclude with a discussion of a novel 'hybrid' method developed recently that yields unitary realizations of the exceptional N=8 and N=7 algebras for all allowed values of their central charges.

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arXiv1996

Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras

We study realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary highest-weight representations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5, respectively. Furthermore, we show that the general coset Ans"atze for the N=8 and N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and SO(7)xU(1)/G_2, respectively, as the additional consistent solutions for certain values of the central charge. The coset space SO(8)/SO(7) is the seven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with torsion, S^7_T. The division algebra of octonions and the associated triality properties of SO(8) play an essential role in all these realizations. We also comment on some possible applications of our results to string theory.

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arXiv1996

Seven Dimensional Octonionic Yang-Mills Instanton and its Extension to an Heterotic String Soliton

We construct an octonionic instanton solution to the seven dimensional Yang-Mills theory based on the exceptional gauge group $G_2$ which is the automorphism group of the division algebra of octonions. This octonionic instanton has an extension to a solitonic two-brane solution of the low energy effective theory of the heterotic string that preserves two of the sixteen supersymmetries and hence corresponds to $N=1$ space-time supersymmetry in the (2+1) dimensions transverse to the seven dimensions where the Yang-Mills instanton is defined.

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arXiv1995

EXTENDED SUPERCONFORMAL SYMMETRY, FREUDENTHAL TRIPLE SYSTEMS AND GAUGED WZW MODELS

We review the construction of extended ( N=2 and N=4 ) superconformal algebras over triple systems and the gauged WZW models invariant under them. The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems (FTS) admit extension to ``maximal'' N=4 SCA's with SU(2)XSU(2)XU(1) symmetry. A detailed study of the construction and classification of N=2 and N=4 SCA's over Freudenthal triple systems is given. We conclude with a study and classification of gauged WZW models with N=4 superconformal symmetry.

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arXiv1993

N=4 Superconformal Algebras and Gauged WZW Models

As shown by Witten the N=1 supersymmetric gauged WZW model based on a group G has an extended N=2 supersymmetry if the gauged subgroup H is so chosen that G/H is Kahler. We extend Witten's result and prove that the N=1 supersymmetric gauged WZW models over G X U(1) are actually invariant under N=4 superconformal transformations if the gauged subgroup H is such that G/HXSU(2) is a quaternionic symmetric space. A previous construction of "maximal" N=4 superconformal algebras with SU(2)XSU(2)XU(1) symmetry is reformulated and further developed so as to relate them to the N=4 gauged WZW models. Based on earlier results we expect the quantization of N=4 gauged WZW models to yield the unitary realizations of maximal N=4 superconformal algebras provided by this construction.

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arXiv1993

Generalized Conformal and Superconformal Group Actions and Jordan Algebras

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems(JTS). These results are extended to Jordan superalgebras and super JTS's. We give the conformal algebras of simple Jordan algebras, hermitian JTS's and the simple Jordan superalgebras as classified by Kac.

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arXiv1992

On the Chiral Rings in N=2 and N=4 Superconformal Algebras

We study the chiral rings in N=2 and N=4 superconformal algebras. The chiral primary states of N=2 superconformal algebras realized over hermitian triple systems are given. Their coset spaces G/H are hermitian symmetric which can be compact or non-compact. In the non-compact case, under the requirement of unitarity of the representations of G we find an infinite set of chiral primary states associated with the holomorphic discrete series representations of G. Further requirement of the unitarity of the corresponding N=2 module truncates this infinite set to a finite subset. The chiral primary states of the N=2 superconformal algebras realized over Freudenthal triple systems are also studied. These algebras have the special property that they admit an extension to N=4 superconformal algebras with the gauge group SU(2)XSU(2)XU(1). We generalize the concept of the chiral rings to N=4 superconformal algebras. We find four different rings associated with each sector (left or right moving). We also show that our analysis yields all the possible rings of N=4 superconformal algebras.

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