Yassen S. Stanev

Chiral asymmetry in four-dimensional open-string vacua

Abstract Starting from the type IIB string on the Z orbifold, we construct some chiral open-string vacua with N = 1 supersymmetry in four dimensions. The Chan-Paton group depends on the (quantized) NS-NS antisymmetric tensor. The largest choice, SO (8) × SU (12) × U (1), has an anomalous U (1) factor whose gauge boson acquires a mass of the order of the string scale. The corresponding open-string spectrum comprises only Neumann strings and includes three families of chiral multiplets in the ( 8, 12 ∗ ) + ( 1, 66 ) representation. A comparison is drawn with a heterotic vacuum with non-standard embedding, and some properties of the low-energy effective field theory are discussed.

Completeness conditions for boundary operators in 2D conformal field theory

Abstract In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of Lewellen on sewing constraints for conformal theories in the presence of boundaries. As a result, we include additional open sectors in the descendants of D odd SU (2) WZW models. A new phenomenon emerges, the appearance of multiplicities and fixed-point ambiguities in the boundary algebra not inherited from the closed sector. We conclude by deriving a set of polynomial equations, similar to those satisfied by the fusion-rule coefficients N ij k , for a new tensor A ab i that determines the open spectrum.

Comments on Gepner models and type I vacua in string theory

We construct open descendants of Gepner models, concentrating mainly on the six-dimensional case, where they give type I vacua with rich patterns of Chan-Paton symmetry breaking and various numbers of tensor multiplets, including zero. We also relate the models in D < 10 without open sectors, recently found by other authors, to the generalized Klein-bottle projections allowed by the crosscap constraint.

Anomalous dimensions in N=4 SYM theory at order g4

We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.

OPEN STRINGS ON THE NEVEU-SCHWARZ 5-BRANE

We analyze the propagation of open and unoriented strings on the Neveu-Schwarz 5-brane (N5-brane) along the lines of a similar analysis for the SU(2) WZNW models. We discuss the two classes of open descendants of the diagonal models and a series of Z2 projected models which exist only for even values of the level k and correspond to branes at D-type orbifold singularities. The resulting configurations of branes and planes are T-dual to those relevant to the study of dualities in super Yang-Mills theories. The association of Chan-Paton factors to D-brane multiplicities is possible in the semi-classical limit k → ∞, but due to strong curvature effects is unclear for finite k. We show that the introduction of a magnetic field implies a twist of the SU(2) current algebra in the open-string sector leading to space-time supersymmetry breaking.

Operator mixing in N=4 SYM: The Konishi anomaly revisited

The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N = 1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one operator, the unintegrated chiral superpotential. In the quantum theory this term receives an admixture by a second operator, the Yang-Mills part of the Lagrangian. It has long been debated whether this “anomalous” contribution is affected by higher loop corrections. We present a first principles calculation at the second non-trivial order in perturbation theory using supersymmetric dimensional reduction as a regulator and renormalisation by Z-factors. Singular higher loop corrections to the renormalisation factor of the Yang-Mills term are required if the conformal properties of two-point functions are to be met. These singularities take the form determined in preceding work on rather general grounds. Moreover, we also find non-vanishing finite terms. The core part of the problem is the evaluation of a four-loop two-point correlator which is accomplished by the Laporta algorithm. Apart from several examples of the T1 topology with two lines of non-integer dimension we need the first few orders in the ǫ expansion of three master integrals. The approach is self-contained in that all the necessary information can be derived from the power counting finiteness of some integrals.

On the logarithmic behaviour in N=4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in = 4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the = 4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.

On the logarithmic behaviour in Script N = 4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in = 4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the = 4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.

Trace formulas for Annuli

Assuming the completeness condition for boundaries we derive trace formulas for the annulus coefficients in 2-dimensional conformal field theory. We also derive polynomial equations that relate the annulus, Moebius and Klein bottle coefficients, and conjecture an annulus trace formula that is sensitive to the orientation of the boundaries.

Open descendants in conformal field theory

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardys ansatz does not apply. It leads to a new tensor with positive integer entries, that satisfies a set of polynomial equations and encodes the classification of the allowed boundary operators.