FUNDAMENTAL INTERACTIONS AND TWISTORLIKE METHODS: XIX Max Born Symposium

Twistors and 2T‐physics
View Description Hide DescriptionTwo‐Time physics applies broadly to the formulation of physics and correctly describes the physical world as we know it. Recently it was applied to a 2T re‐formulation of the d = 4 twistor superstring, which was suggested by Witten as an efficient approach for computations of physical processes in the maximally supersymmetric N = 4 Yang‐Mills field theory in four dimensions. The 2T formalism provides a six dimensional view of this theory and suggests the existence of other d = 4 dual forms of the same theory. Furthermore the 2T approach led to the first formulation of a twistor superstring in d = 10 appropriate for AdS_{5}×S^{5} backgrounds, and a twistor superstring in d = 6 related to the little understood superconformal theory in d = 6. The proper generalization of twistors to higher dimensions is an essential ingredient which is provided naturally by 2T‐physics. These developments are summarized in this lecture.

Relativistic Spinor Dynamics Inducing the Extended Lorentz‐Force‐Like Equation
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Two‐Twistor Space, Commuting Composite Minkowski Coordinates and Particle Dynamics
View Description Hide DescriptionWe employ the modification of the basic Penrose formula in twistor theory, which allows to introduce commuting composite space‐time coordinates. It appears that in the course of such modification the internal symmetry SU (2) of two‐twistor system is broken to U(1). We consider the symplectic form on two‐twistor space, permitting to interpret its 16 real components as a phase‐space. After a suitable change of variables such a two‐twistor phase space is split into three mutually commuting parts, describing respectively the standard relativistic phase space (8 degrees of freedom), the spin sector (6 degrees of freedom) and the canonical pair angle‐charge describing the electric charge sector (2 degrees of freedom). We obtain a geometric framework providing a twistor‐inspired 18‐dimensional extended relativistic phase space M ^{18}. In such a space we propose the action only with first class constraints, describing the relativistic particle characterized by mass, spin and electric charge.

Twistor Cosmology and Quantum Space‐Time
View Description Hide DescriptionThe purpose of this paper is to present a model of a ‘quantum space‐time’ in which the global symmetries of space‐time are unified in a coherent manner with the internal symmetries associated with the state space of quantum‐mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space‐time imply that the pseudo‐Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space‐time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space‐time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen‐dimensional analogue of the Friedmann‐Robertson‐Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space‐time is an even perfect square, there exists a canonical way of breaking the global quantum space‐time symmetry so that a generic point of quantum space‐time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space‐time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space‐time description is an emergent feature arising as a consequence of a quantum averaging over the internal degrees of freedom. The familiar probabilistic features of the quantum state, represented by properties of the density matrix, can then be seen as a by‐product of the causal structure of quantum space‐time.

AdS Twistors for Higher Spin Theory
View Description Hide DescriptionWe construct spectra of supersymmetric higher spin theories in D = 4, 5 and 7 from twistors describing massless (super‐)particles on AdS spaces. A massless twistor transform is derived in a geometric way from classical kinematics. Relaxing the spin‐shell constraints on twistor space gives an infinite tower of massless states of a “higher spin particle”, generalizing previous work of Bandos et al.. This can generically be done in a number of ways, each defining the states of a distinct higher spin theory, and the method provides a systematic way of finding these. We reproduce known results in D = 4, minimal supersymmetric 5‐ and 7‐dimensional models, as well as supersymmetrisations of Vasiliev’s Sp‐models as special cases. In the latter models a dimensional enhancement takes place, meaning that the theory lives on a space of higher dimension than the original AdS space, and becomes a theory of doubletons. This talk was presented at the XIX‐th Max Born Symposium “Fundamental Interactions and Twistor‐Like Methods”, September 2004, in Wrocław, Poland.

Twistor Transform for Spinning Particle
View Description Hide DescriptionTwistorial formulation of a particle of arbitrary spin has been constructed. The twistor formulation is deduced from a space‐time formulation of the spinning particle by introducing pure gauge Lorentz harmonics in this system. Canonical transformations and gauge fixing conditions, excluding space‐time variables, produce the fundamental conditions of twistor transform relating the space‐time formulation and twistor one. Integral transformations, relating massive twistor fields with usual space‐time fields, have been constructed.

Complex Minkowski Space as a Conformal Phase Space
View Description Hide DescriptionThe complex Minkowski phase space has the physical interpretation as the phase space of the scalar massive conformal particles. The aim of this presentation is the construction and investigation of the quantum complex Minkowski space.

BPS Preons in Supergravity and Higher Spin Theories. An Overview From the Hill of Twistor Approach
View Description Hide DescriptionWe review briefly the notion of BPS preons, first introduced in 11‐dimensional context as hypothetical constituents of M‐theory, in its generalization to arbitrary dimensions and emphasizing the relation with twistor approach. In particular, the use of a “twistor‐like” definition of BPS preon (almost) allows us to remove supersymmetry arguments from the discussion of the relation of the preons with higher spin theories and also of the treatment of BPS preons as constituents. We turn to the supersymmetry in the second part of this contribution, where we complete the algebraic discussion with supersymmetric arguments based on the M‐algebra (generalized Poincaré superalgebra), discuss the possible generalization of BPS preons related to the osp(1n) (generalized AdS) superalgebra, review a twistor‐like κ‐symmetric superparticle in tensorial superspace, which provides a point‐like dynamical model for BPS preon, and the rôle of BPS preons in the analysis of supergravity solutions. Finally we describe resent results on the concise superfield description of the higher spin field equations and on superfield supergravity in tensorial superspaces.

Introduction to the Classical Theory of Higher Spins
View Description Hide DescriptionWe review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.

Quantum BRST Charge and OSp(18) Superalgebra of Twistor‐Like p‐branes with Exotic Supersymmetry and Weyl Symmetry
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Brane Solutions of Gravity‐Dilaton‐Axion Systems
View Description Hide DescriptionWe consider general properties of brane solutions of gravity‐dilaton‐axion systems. We focus on the case of 7‐branes and instantons. In both cases we show that besides the standard solutions there are new deformed solutions whose charges take value in any of the three conjugacy classes of SL(2, R). In the case of 7‐branes we find that for each conjugacy class the 7‐brane solutions are 1/2 BPS. Next, we discuss the relation of the 7‐branes with the DW/QFT correspondence. In particular, we show that the two (inequivalent) 7‐brane solutions in the SO(2) conjugacy class have a nice interpretation as a distribution of (the so‐called near horizon limit of) branes. This suggests a way to define the near‐horizon limit of a 7‐brane.
In the case of instantons only the solutions corresponding to the R conjugacy class are 1/2 BPS. The solutions corresponding to the other two conjugacy classess correspond to non‐extremal deformations. We first discuss an alternative description of these solutions as the geodesic motion of a particle in a two‐dimensional AdS _{2} space. Next, we discuss the instanton‐soliton correspondence. In particular, we show that for two of the conjugacy classes the instanton action in D dimensions is given by the mass of the corresponding soliton which is a (non‐extremal) black hole solution in D+1 dimension. We speculate on the role of the non‐extremal instantons in calculating higher‐derivative corrections to the string effective action and, after a generalization from a flat to a curved AdS _{5} background, on their role in the AdS/CFT corresopondence.

Superbranes, D = 11 CJS Supergravity and Enlarged Superspace Coordinates/Fields Correspondence
View Description Hide DescriptionWe discuss the rôle of enlarged superspaces in two seemingly different contexts, the structure of the p‐brane actions and that of the Cremmer‐Julia‐Scherk eleven‐dimensional supergravity. Both provide examples of a common principle: the existence of an enlarged superspaces coordinates/fields correspondence by which all the (worldvolume or spacetime) fields of the theory are associated to coordinates of enlarged superspaces. In the context of p‐branes, enlarged superspaces may be used to construct manifestly supersymmetry‐invariant Wess‐Zumino terms and as a way of expressing the Born‐Infeld worldvolume fields of D‐branes and the worldvolume M5‐brane two‐form in terms of fields associated to the coordinates of these enlarged superspaces. This is tantamount to saying that the Born‐Infeld fields have a superspace origin, as do the other worldvolume fields, and that they have a composite structure. In D=11 supergravity theory enlarged superspaces arise when its underlying gauge structure is investigated and, as a result, the composite nature of the A _{3} field is revealed: there is a full one‐parametric family of enlarged superspace groups that solve the problem of expressing A _{3} in terms of spacetime fields associated to their coordinates. The corresponding enlarged supersymmetry algebras turn out to be deformations of an expansion of the osp(132) algebra. The unifying mathematical structure underlying all these facts is the cohomology of the supersymmetry algebras involved.

Unitary Realizations of U‐duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
View Description Hide DescriptionWe review the current status of the construction of unitary representations of U‐duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal N = 8 supergravity theories and on the N = 2 Maxwell‐Einstein supergravity (MESGT) theories defined by Jordan algebras of degree three in five dimensions and their descendants in four and three dimensions. Entropies of the extremal black hole solutions of these theories in five and four dimensions are given by certain invariants of their U‐duality groups. The five dimensional U‐duality groups admit extensions to spectrum generating generalized conformal groups which are isomorphic to the U‐duality groups of corresponding four dimensional theories. Similarly, the U‐duality groups of four dimensional theories admit extensions to spectrum generating quasiconformal groups that are isomorphic to the corresponding U‐duality groups in three dimensions. For example, the group E _{8(8)} can be realized as a quasiconformal group in the 57 dimensional charge‐entropy space of BPS black hole solutions of maximal N = 8 supergravity in four dimensions and leaves invariant “lightlike separations” with respect to a quartic norm. Similarly E _{7(7)} acts as a generalized conformal group in the 27 dimensional charge space of BPS black hole solutions in five dimensional N = 8 supergravity and leaves invariant “lightlike separations” with respect to a cubic norm. For the exceptional N = 2 Maxwell‐Einstein supergravity theory the corresponding quasiconformal and conformal groups are E _{8(−24)} and E _{7(−25)}, respectively. We outline the oscillator construction of the unitary representations of generalized conformal groups that admit positive energy representations, which include the U‐duality groups of N = 2 MESGT’s in four dimensions . We conclude with a review of the minimal unitary realizations of U‐duality groups that are obtained by quantizations of their quasiconformal actions and discuss in detail the minimal unitary realization of E _{8(8)}.

Non‐Anticommutative Deformations of Gauge Fields and Hypermultiplets in N=(1,1) Superspace
View Description Hide DescriptionWe overview the SO(4)×SU(2) invariant and N=(1,0) supersymmetry‐preserving non‐anticommutative deformations of the Euclidean N=(1,1) supersymmetric gauge theories and hypermultiplets (neutral and charged) interacting with an abelian gauge multiplet, starting from their off‐shell formulation in N=(1,1) harmonic superspace. The corresponding component actions are presented and the Seiberg‐Witten‐type transformations to the undeformed component fields are explicitly given. Mass terms and scalar potentials for the hypermultiplets can be generated via the Scherk‐Schwarz mechanism and Fayet‐Iliopoulos term in analogy to the undeformed case. The neutral hypermultiplet action is invariant under N=(2,0) supersymmetry and describes a deformed N=(2,2) gauge theory. The string theory origin of the considered singlet deformation is exhibited.

Canonical Quantization and Black Hole Perturbations
View Description Hide DescriptionWe examine the possibility of a constraint‐free quantization of linearized gravity, based on the Teukolsky equation for black hole perturbations.
We exhibit a simple quadratic (but complex) Lagrangian for the Teukolsky equation, leading to the interpretation that the elementary excitations (gravitons bound to the Kerr black hole) are unstable.

Quaternionic and Octonionic Spinors
View Description Hide DescriptionQuaternionic and octonionic spinors are introduced and their fundamental properties (such as the space‐times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and octonionic supersymmetric algebras defined in terms of such spinors are constructed. Specializing to the D = 11‐dimensional case, the relation of both the quaternionic and the octonionic supersymmetries with the ordinary M‐algebra are discussed.

Obituary—Perjés Zoltán (1943–2004)
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Back Matter
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