Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

Abstract

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings Bergshoeff, Eric; Randjbar-Daemi, S.; Salam, A.; Sarmadi, H.; Sezgin, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. We construct an N = 1 locally supersymmetnc o-model with a Wess-Zummo term coupled to supergravity m two dimensions. If one takes the o-model mamfold to be the product of d-d~mensmnal Minkowski space M a and a group mamfold G, and if the radms of G is quantized m appropriate umts of the stnng tensmn, then the model descnbes a Neveu-Schwarz-Ramond (NSR)-type string mowng on M d × G (Our model generahzes earlier work of refs. [1,2] which do not contain a Wess-Zumino term and that of refs [5,6] which is not locally supersymmetnc ) The zwetbein and the gravitmo field equations yteld constraints which generahze those of the NSR model to the case of a non-abelian group mamfold In particular, the fenmomc constraint contains a new term tnlinear m the fermiomc fields We quantize the theory in the light-cone gauge and derive the critical dimensions. We compute the mass spectrum of a closed stnng moving on M a × G and show that massless fermmns do not arise for non-abdian G for the spmmng stnng, in agreement with the result of Friedan and Shenker [22] * Supported by Swiss National Funds.

(8,0) Locally supersymmetric sigma models with conformal invariance in two dimensions

“…where A. "s is a composite gauge field for some Yang-Mllls gauge group where we have introduced the gravitational coupling constant x Consequently, in the global supersymmetry limit both curvatures vanish since x goes to zero In that limit the fields (r,z) decouple from the physical scalar multlplet fields (0%~u~), and can con-Slstently be set equal to (1,0) The lagrangmn then reduces to free kinetic terms for (0%~ ,a) This lagranglan coincides with the one given in ref [20] which describes the field theory of the AdS3 singleton multiplet (b) We expect that the (8,0) conformal supergravity theory described in this paper corresponds to the gauge theory of the conformal superalgebra 0Sp (2,8) ~0Sp (2,8) [21 ] (c) In the conformal gauge ~ = 1 and 2 = 0, the (8,0) model for n=0 and without the heterotlc fertalons coincides with the model one would obtain by dimensional reduction and subsequent chIral truncation of the N= 8, d= 3 Poincar6 supergravlty model of Marcus and Schwarz [16] This is remarkable because the compensating fields ~ and 2 belong to the conformal supermultlplet itself, as opposed to being independent matter fields as is usually the case in a Brans-Dicke type theory The only other known conformal supergravitles which contain their own compensators are the conformal supergravlty in d=10 [15] and in d=6 [22] (d) In view of the previous remark, since an N= 16 Poincar6 supergravlty theory coupled to Es/SO (16) scalar manifold exists in three dimensions, we expect that an (16,0) model in two dimensions where the matter scalars parametnze the coset Es/SO (l 6) and action similar to that given in section 3 can be constructed However such a model probably only exists on-shell, since the off-shell (16,0) superconformal multlplet contains a large number of components with undesirable canonical dimensions which makes the construction of an action highly nontrivial (e) The signature of the metric gap has 8m positive, and 8n negative signs which do not correspond to a lorentzian signature An intriguing possibility might be that, say, for m=0, the 8n scalars of the theory, together with the unphysical scalars r and ~o form the coordinates of a special (8n + 2)-dimensional mamfold with lorentzmn signature (f) We expect that a Wess-Zummo term can be added to the (8,0) model of this paper, in much the same way it is added m the (4,0) model [ 10] (g) It seems conceivable that one can gauge any subgroup of the global SO (8 + n,m) group by introducing an (8,0) Yang-Mdls multlplet (Au, O, where ( Is an elght-spmor of SO (8) This would work in a similar way as m ref [4] (h) From the (8,0) model, by truncauon, one can obtain a (2,0) model with the field content (e~ m, ~u~',A~,, 2', ~) where t= 1, 2 is an SO(2) index Here the vector field A~ has only one gauge transformation It is interesting to compare th~s theory wxth the one based on the superconformal multlplet (e~ m, ~uu', B~,) where the vector field B~, has two independent gauge transformations [ 8 ] (1) Concerning the anomahes, the perturbative Lorentz anomaly m two dimensions will be absent provided that the number ofheterotlc fermions ~ r is fixed ...…”

“…Having possible stnng apphcatlons m mind, it is clearly of interest to mqmre as to whether one can construct (p,q) models w~th p, q> 4 From the work of Alvarez-Gaum6 and Freedman [ 14] it is known that globally supersymmetnc sigma models exist only for p,q<~ 4 On the other hand, the dimensional reduction of ten-dimensional Yang--Mills coupled conformal supergrawty [ 15 ] to two t Present address Department of Physics, Brandeis Umverslty, Waltham, MA 02254, USA :~ For the (1,1) model see refs [1][2][3], for the (1,0) an (2,0) models see refs [4][5][6][7], for the (2,2) model see ref [8], the (4,4) model was considered m ref [9], the (4,0) model with Wess-Zummo term is given in ref [ 10] :2 By (p,q) supersymmetry we mean a supersymmetry algebra generated by p left-handed and q right-handed supersymmetry generators [11][12][13] 0370-2693/87/$ 03 50 © Elsevier Science Pubhshers B V (North-Holland Physics Pubhshlng Division) dimensions is expected to give an (8,8) or (8,0) conformal supergravaty coupled to scalar multlplets This suggests that, m order to construct (p,q) models w~th p,q> 4, one should consider the local supersymmetry as an essentml ingredient of the theory This is despite the fact that the fields of the supergrawty multlplet do not have dynamics in two d~menslons In fact, a similar situation arises in three dimensions, where the construction of N= 8 or N= 16 s~gma models reqmres the coupling of a non-dynamical supergravlty multlplet [ 16 ] In this letter, we indeed construct an action for an (8,0) locally supersymmetrlc sigma model Our strategy in this construction is as follows We first extract the field content of the (8,0) superconformal multlplet, and the matter scalar mulUplet by dimensional reduction of ten-d~mensxonal conformal supergravlty [ 15 ], and Yang-Mdls multlplet [ 17 ], respectwely We then construct the transformaUon rules and the action of the two...…”

SYMMETRIES OF p-BRANES

“…where k p is a normalization constant, depending on the group G, which we will not specify (for the case p = 1 see, for example, [12] The functional C defined in (2.6) can be computed explicitly in the cases p = 1, 3, 5 by substituting (A.2) into (2.6). We get …”

Kac–Moody and Virasoro symmetries of principal chiral sigma models

“…For example, string theory on a product of d-dimensional Minkowski spacetime with a group manifold of suitable dimension is described by an exactly-solvable principal sigma model (PCM) with a critical Wess-Zumino term that makes the model conformally invariant at the quantum level [1]. The world-sheet supersymmetric version of the model, namely the spinning string on a group manifold, has also been studied [2].…”

“…It is known that a symmetric space sigma model (SSM), in which the scalar fields of a two-dimensional theory live on a symmetric coset space G/H, has a Kac-Moody symmetry G [17]. Now the PCM for a group manifold G can be equivalently viewed as an SSM for the symmetric coset space (G× G)/G, and therefore from the known results for the SSM, it must be that the PCM has the symmetry G × G. 2 One of the main purposes of the present paper is to give an explicit construction of the full G× G symmetry transformations for the PCM. Whilst this obviously contains G × G as a subalgebra, this is, as we shall discuss in appendix A, different from the G × G symmetry that was claimed in [12,4].…”