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In the past ** A.A. Tseytlin** has collaborated on articles with

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AbstractWe explicitly prove that d = 4 theory following via reduction from N = 1, d = 10 supergravities is not finite at one loop, while the version of N = 8 supergravity directly following from N = 1, d = 11 theory is one-loop finite. The method we use is based on quantization of initial higher dimensional theory as a first step. The results also suggest the possible existence of non-standard (higher N) d > 4 supergravities which reduce to d = 4 theories with finite N = 8 supergravity sector.

AbstractWe compute the effective action for an abelian vector field coupled to the virtual open Bose string. The problem is exactly solved (in the “tree” and “one-loop” approximation for the string theory) for the case of a constant field strength and the number of space-time dimensions D=26. The resulting tree-level effective lagrangian is shown to coincide with the Born-Infeld lagrangian, [det(δμν + 2Πα′Fμν)]12.

AbstractWe discuss the cancellation of Weyl and local Lorents anomalies in two-dimensional chiral N ⩽ 2 supergravity-matter systems. There exists a unique anomaly-free model with N = 12 supersymmetry which corresponds to the heterotic string (with the critical dimension D = 10) in the same way as the anomaly-free models with non-chiral N = 0, 1 and 2 supersymmetries correspond to the string theories with D = 26, 10 and 2. The only two other anomaly-free models have chiral N = 1++ and N = 32++− supersymmetries and correspond to two new “heterotic” string theories with D = 2.

AbstractWe present a covariant definition of the effective action Γ for fields corresponding to different string excitations (scalar, metric, antisymmetric tensor, …) in terms of a string path integral with “external sources”. The problem of deriving the gravitational part of Γ is reduced to that of establishing the effective action for a generalized σ-model on a curved two-dimensional background and subsequent integration over two-metrics. The low-energy approximation for Γ is computed.

AbstractWe point out that there is an ambiguity in some of the coefficients in the “low-energy” effective action (EA) for the massless string modes (in particular, the coefficients of the Rμν2- and R2-terms in the gravitational EA's are ambiguous). In the S-matrix approach this ambiguity is a consequence of an off-shell ambiguity in the subtraction of the massless exchanges (manifesting itself as a freedom of field redefinitions which leave the S-matrix invariant because of the equivalence theorem). In the world-sheet path integral approach the ambiguity is due to the freedom in the choice of a 2D renormalization scheme and a Weyl gauge. We also comment on the relation with the second-quantized string approach.

AbstractCorrecting the previous claim by one of the authors it is shown (using the partition function approach) that the effective action of the open superstring theory coincides (in the abelian and Fμν = const. limit) with the Born-Infeld action. In the second part of the work we construct the order F6 supersymmetric extension of the D = 10 Maxwell theory. We find that the F4 + F6 terms in the action can be uniquely determined from the requirement of the D = 10 supersymmetry and precisely coincide with the terms appearing in the expansion of the Born-Infeld action.

AbstractWe develop a manifestly covariant procedure of computation of the partitionfunction Z of a general renormalizable 2D sigma model defined on a compact two-space. Special attention is paid to a proper separation of the path integral into the integrals over the constant and nonconstant parts of the coordinate. The important role of the path integral measure in establishing the covariance and renormalizability properties of Z is stressed. We explicitly check the validity of the representation of the closed string effective action as the partial derivative of Z over the logarithm of the cutoff. We also comment on the status of the “c-theorem” and suggest a resolution of a problem in the renormalization of the closed string loop corrections corresponding to the disc topology.

AbstractGiven a static string solution with some free constant parameters (“moduli”) it may be possible to construct a time-dependent solution by just replacing the moduli by some functions of time. We present several examples when such a “rolling moduli” ansatz is consistent. In particular, the anisotropic D=4 cosmological solution of Nappi and Witten can be reinterpreted as a time-dependent generalisation of the (analytic continuation of the) D=3 “charged black string” background with the “charge” changing with time. We find some new D=4 cosmological solutions which are “two rolling moduli” generalisations of the previously known ones. We also comment on the interplay between duality transformations and the replacement of moduli by functions of time.

AbstractWe analyze the recently proposed definition of the off-shell, gauge-invariant, gauge-independent, effective action Γ, utilizing an invariant metric on the field space. It is shown how to establish correspondence between Γ and the standard effective action, calculated in some particular (Landau-type) gauge. Several examples are explicitly discussed, including Yang-Mills theory, the effective potential in scalar QED, and one-loop quantum gravity. Generalization to the case of super-invariant theories (e.g. super-Yang-Mills and supergravity) is also presented.

AbstractAspects of string cosmology for critical and non-critical strings are discussed emphasizing the necessity to account for the dilaton dynamics for a proper incorporation of “large-small” duality. This drastically modifies the intuition one has with Einstein's gravity. For example winding modes, even though contributing to the energy density, oppose expansion and if not annihilated will stop the expansion. Moreover we find that the radiation dominated era of the standard cosmology emerges quite naturally in string cosmology. Our analysis of non-critical string cosmology provides a reinterpretation of the (universal cover of the) recently studied two-dimensional black hole solution as a conformal realization of cosmological solutions found previously by Mueller.

AbstractWe compare order R4 terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories. Some of these terms do not receive higher-loop corrections being related by supersymmetry to ‘anomaly-cancelling’ terms which depend on the antisymmetric 2-tensor. At the same time, the consistency of duality relation implies that the ‘tree-level’ R4 super-invariant (the one which has ζ(3)-coefficient in the sphere part of the action) should appear also at higher orders of loop expansion, i.e. should be multiplied by a non-trivial function of the dilaton.

AbstractWe carry out a thorough survey of entropy for a large class of p-branes in various dimensions. We find that the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic p-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic p-branes is non-vanishing only for solutions preserving 18 of the original supersymmetries. Upon toroidal compactification these reduce to dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6 dimensions, which preserves 14 of the original supersymmetries, the near-extremal entropy is found to agree with a world sheet calculation, in support of the existing literature. The remaining 3 interesting cases preserve 12 of the original supersymmetries. These are the self-dual 3-brave in 10 dimensions, and the 2- and 5-braves in 11 dimensions. For all of them the scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking temperature is in agreement with a statistical description in terms of free massless fields on the world volume.

AbstractWe discuss the known microscopic interpretations of the Bekenstein-Hawking entropy for configurations of intersecting M-branes. In some cases the entropy scales as that of a massless field theory on the intersection. A different situation, found for configurations which reduce to 1-charge D = 5 black holes or 2-charge D = 4 black holes, is explained by a gas of non-critical strings at their Hagedorn temperature. We further suggest that the entropy of configurations reducing to 1-charge D = 4 black holes is due to 3-branes moving within 5-branes.

AbstractWe consider an Abelian N=4 super Yang–Mills theory coupled to background N=4 conformal supergravity fields. At the classical level, this coupling is invariant under global SU(1,1) transformation of the complex (“dilaton–axion”) supergravity scalar combined with an on-shell N=4 vector–vector duality. We compute the divergent part of the corresponding quantum effective action found by integrating over the super Yang–Mills fields and demonstrate its SU(1,1) invariance. This divergent part related to the conformal anomaly is one-loop exact and should be given by the N=4 conformal supergravity action containing the Weyl tensor squared term. This allows us to determine the full non-linear form of the bosonic part of the N=4 conformal supergravity action which has manifest SU(1,1) invariance.

AbstractWe compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of N=4 SYM theory in 4 dimensions, assuming that the gauge group SU(N+1) is broken to SU(N)×U(1) by a constant scalar background X. While the leading 1-loop correction is the familiar c1F4/|X|4 term, the 2-loop expression starts with c2F6/|X|8. The 1-loop constant c1 is known to be equal to the coefficient of the F4 term in the Born–Infeld action for a probe D3-brane separated by distance |X| from a large number N of coincident D3-branes. We show that the same is true also for the 2-loop constant c2: it matches the coefficient of the F6 term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the F6 term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the v6 term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the (1+0)-dimensional reduction of N=4 SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory—supergravity correspondence for higher order (F8, etc.) terms.

AbstractWe show that solitonic solutions of the classical string action on the AdS5×S5 background that carry charges (spins) of the Cartan subalgebra of the global symmetry group can be classified in terms of periodic solutions of the Neumann integrable system. We derive equations which determine the energy of these solitons as a function of spins. In the limit of large spins J, the first subleading 1/J coefficient in the expansion of the string energy is expected to be non-renormalized to all orders in the inverse string tension expansion and thus can be directly compared to the 1-loop anomalous dimensions of the corresponding composite operators in N=4 super-YM theory. We obtain a closed system of equations that determines this subleading coefficient and, therefore, the 1-loop anomalous dimensions of the dual SYM operators. We expect that an equivalent system of equations should follow from the thermodynamic limit of the algebraic Bethe ansatz for the SO(6) spin chain derived from SYM theory. We also identify a particular string solution whose classical energy exactly reproduces the one-loop anomalous dimension of a certain set of SYM operators with two independent R charges J1, J2.

AbstractWe investigate the structure of the dilatation operator D of planar N=4 SYM in the sector of single trace operators built out of two chiral combinations of the 6 scalars. Previous results at low orders in 't Hooft coupling λ suggest that D has a form of an SU(2) spin chain Hamiltonian with long range multiple spin interactions. Instead of the usual perturbative expansion in powers of λ, we split D into parts D(n) according to the number n of independent pairwise interactions between spins at different sites. We determine the coefficients of spin–spin interaction terms in D(1) by imposing the condition of regularity of the BMN-type scaling limit. For long spin chains, these coefficients turn out to be expressible in terms of hypergeometric functions of λ, which have regular expansions at both small and large values of λ. This suggest that anomalous dimensions of “long” operators in the two-scalar sector should generically scale as λ at large λ, i.e., in the same way as energies of semiclassical states in dual AdS5×S5 string theory.

AbstractWe consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS5×S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters γi which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N=4 SYM theory, but with scalar and Yukawa interactions “deformed” by γi-dependent phases. The special case of equal γi=γ corresponds to the N=1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal γi this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective “Landau–Lifshitz” actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e., it allows one to capture the right vacuum states and the “macroscopic spin wave” sector of states of the spin chain in the continuum coherent state effective action.

AbstractWe compute 1-loop correction E1 to the energy of folded string in AdS5×S5 (carrying spin S in AdS5 and momentum J in S5) using a “long string” approximation in which S≫J≫1. According to the AdS/CFT the function E1 should represent first subleading correction to strong coupling expansion of anomalous dimension of higher twist SL(2) sector operators of the form TrDSZJ. We show that E1 smoothly interpolates between the lnS regime (previously found in the J→0 case) and the λ/J2ln3(S/J) regime (which is the leading correction to the thermodynamic limit on the spin chain side). This supports the universality of the lnS scaling. As in the previous work, we also find “non-analytic” corrections related to non-trivial 1-loop phase in the corresponding Bethe ansatz S-matrix.

AbstractAn important “observable” of planar N=4 SYM theory is the scaling function f(λ) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of light-like Wilson loop. The non-trivial relation between the anomalous dimension and the Wilson loop interpretations of f(λ) is well-understood on the perturbative gauge theory side of the AdS/CFT duality. In the first part of this paper we present the dual string-theory counterpart of this relation, i.e., the equivalence between the closed-string and the open-string origins of f(λ). We argue that the coefficient of the logS term in the energy of the closed string with large spin S in AdS5 should be equal to the coefficient in the logarithm of expectation value of the null cusp Wilson loop, to all orders in λ−1/2 expansion. The reason is that the corresponding minimal surfaces happen to be related by a conformal transformation (and an analytic continuation). As a check, we explicitly compute the leading 1-loop string sigma model correction to the cusp Wilson loop, reproducing the same subleading coefficient in f(λ) as found earlier in the spinning closed string case. The same function f(λ) appears also in the resummed form of the 4-gluon amplitude as discussed at weak coupling by Bern, Dixon and Smirnov and recently found at the leading order at strong coupling by Alday and Maldacena (AM). Here we attempt to extend the latter approach to a subleading order in λ−1/2 by computing the IR singular part of the 1-loop string correction to the corresponding T-dual Wilson loop. We discuss explicitly the 1-cusp case and comment on apparent problems with the dimensional regularization proposal of AM when directly applied order by order in strong coupling (string inverse tension) expansion.

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