Bosonic Background Research Articles

Holographic renormalization group flow, Wilson loops and field-theory -functions

We study the Renormalization Group (RG) flow of critical bosonic background fields in the framework of the RG approach to string theory. In this approach quantum field theory beta-functions are the extra inputs in solving the string theory sigma-model equations. We study two different situations, the first one is the Yang-Mills theory where the coupling constant diverges in the infrared limit. The second case corresponds to a type of theories where the beta-function has a pole in the infrared limit and it changes sign through the pole (as in N=1 super-Yang-Mills theory). For this case in the strong coupling branch, in the infrared, there is an interval of values of the coupling in which the theory only leads to confinement. We have obtained this range. We also mention the theories with conformal-fixed points and their relation to theories with a pole in the beta-functions. We calculate the Wilson loops in these theories.

T-duality covariance of SuperD-branes

T-duality realized on SuperD-brane effective actions probing in constant $G_{mn}$ and $b_{mn}$ backgrounds is studied from a pure world volume point of view. It is proved that requiring {\em T-duality covariance} of such actions ``fixes'' the T-duality transformations of the world volume dynamical fields, and consequently, of the NS-NS and R-R coupling superfields. The analysis is extended to uncover the mapping of the symmetry structure associated with these SuperD-brane actions. In particular, we determine the T-duality transformation properties of kappa symmetry and supersymmetry, which allow us to prove that bosonic supersymmetric world volume solitons of the original theory generate, through T-duality, the expected ones in the T-dual theory. The latter proof is generalized to arbitrary bosonic backgrounds. We conclude with some comments on extensions of our approach to arbitrary kappa symmetric backgrounds, non-BPS D-branes and non-abelian SuperD-branes.

A note on a relation between the Killing spinor and Einstein equations

It is shown that, under certain conditions, the existence of a Killing spinor on a bosonic background of a supergravity theory implies that the Einstein equations are also satisfied. As an application of the theorem, we obtain a new black fivebrane solution of D=11 supergravity, which has K3× R topology and preserves 1/4th supersymmetries of the theory.

Quantum cosmology in the models of 2D and 4D dilatonic supergravity with WZ matter

We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the corresponding action on a bosonic background is constructed and the interaction with $N$ (dilatonic) Wess-Zumino (WZ) multiplets is presented. Working in the large-N approximation, it is enough to consider the trace anomaly induced effective action due to dilaton-coupled conformal matter as a quantum correction (for 2d models s-waves approximation is additionally used). The equations of motion for all such models with quantum corrections are written in a form convenient for numerical analysis. Their solutions are numerically investigated for 2d and 4d Friedmann-Robertson-Walker (FRW) or 4d Kantowski-Sacks Universes with a time-dependent dilaton via exponential dilaton coupling. The evolution of the corresponding quantum cosmological models is given for different choices of initial conditions and theory parameters. In most cases we find quantum singular Universes. Nevertheless, there are examples of Universe non-singular at early times. Hence, it looks unlikely that quantum matter back reaction on dilatonic background (at least in large $N$ approximation) may really help to solve the singularity problem.

Special conformal symmetry of worldvolume actions

Kappa-symmetric worldvolume actions of the D3-, M5-, and M2-branes can be coupled consistently to their near horizon bosonic geometry background. We study the gauge-fixed action in the approximation in which only the transverse radial direction of the brane is allowed to fluctuate. The generalized special conformal symmetry of these self-interacting actions is established. This opens up the possibility to find out if the full superconformal symmetry of the free actions of these branes survives in the presence of coupling defined by the size of the anti--de Sitter throat.

Trace anomaly induced effective action and 2D black holes for dilaton coupled supersymmetric theories

The action for two-dimensional (2D) dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. A trace anomaly and anomaly induced effective action (in components as well as in supersymmetric form) for a matter supermultiplet on a bosonic background are found. The one-loop effective action and large-$N$ effective action for quantum dilatonic supergravity are also calculated. Using an induced effective action one can estimate the back reaction of dilaton coupled matter to the classical black hole solutions of dilatonic supergravity. That is done on the example of a supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. A similar 2D analysis may be used to study spherically symmetric collapse for other models of 4D supergravity.

One-loop supergravity corrections to black hole entropy and residual supersymmetry

We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hole. In the extreme case the contributions from graviton, gravitino and photon to the one-loop corrections to the entropy are shown to cancel. This gives the first explicit example of the supersymmetric non-renormalization theorem for the on-shell action (entropy) for BPS configurations which admit Killing spinors. We display the residual supersymmetry of the perturbations of a general supersymmetric theory in a bosonic BPS background.

U-duality symmetries from the membrane world-volume

We study U-duality symmetries of toroidally compactified M-theory from the membrane world-volume point of view. This is done taking the most general set of bosonic background fields into account. Upon restriction to pure moduli backgrounds, we are able to find the correct U-duality groups and moduli coset parameterizations for dimensions D > 6 as symmetries of the membrane world-volume theory. In particular, we derive the D = 8 U-duality group SL(2) × SL(3). For general background fields, we concentrate on the case D = 8. Though the SL(2) part of the symmetry appears to be obstructed by certain terms in the equations of motion, we are able to read off the transformation properties for the background fields. These transformations are verified by comparison with 11-dimensional supergravity dimensionally reduced to D = 8.

A truly crazy idea about type-IIB supergravity and heterotic sigma-models

Within the confines of the standard NSR sigma-model approach, we construct an explicit and manifestly (1,0) heterotic sigma-model where the bosonic background fields are those of 10D, N = IIB supergravity. The novelty that permits this construction is to use the righton sector of the (1,0) NSR sigma-model to describe the currents of the positive chiral part of the SO(1,9) spin-bundle tensored with itself.

Four-dimensional plane wave string solutions with coset CFT description

We present a number of D = 4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by ‘boosting’ the twisted products of two D = 2 ‘cosmological’ or ‘black-hole’ cosets related to (G ⊗ G′)/(H ⊗ H′) (G, G′ = SL(2, R) or SU(2); H, H ′ = SO(1, 1) or SO(2)) gauged WZW models. We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with known string backgrounds. By applying a non-abelian duality transformation to the NW model we find a D = 4 solution which admits a covariantly constant null Killing vector but is not a plane wave. Higher dimensional bosonic backgrounds with isometries can be interpreted as lower dimensional ones with extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents also a D = 3 gravi-electromagnetic heterotic string plane wave. In addition to the (1, 1) supersymmetric embeddings of bosonic solutions we construct a number of non-trivial (1, 0) supersymmetric exact D = 4 heterotic string plane wave solutions some of which are related (by a boost and analytic continuation) to limiting cases of D = 4 heterotic black hole solutions.

Superstring propagation through supergravitational shockwaves

In all previous works on strings (and superstrings) in curved space-times, explicit calculations were performed only in purely bosonic gravitational backgrounds. Here, we propose to introduce a background containing also fermionic degrees of freedom, solution of the N = 1 supergravity equations in D dimensions. We find an explicit N = 1 linearized supergravity shockwave solution giving the spin-3/2 Rarita-Schwinger field, and an exact (full non-linear) gravitational shockwave bosonic part. We study a Green-Schwarz superstring propagating in such a supergravity background. We write and solve the superstring equations. Contrarely to the purely bosonic shockwave case (in which spinor-string propagation is free), spinor-string coordinates couple here non-trivially to the transverse bosonic coordinates through the fermionic background. We find that outgoing fermionic-modes are mixed with ingoing bosonic (and fermionic) modes. This leads to a new feature of particle transmutation between bosons and fermions, described by the superstring ground states (and also by the excited states). The presence of the bosonic-fermionic background provides in string theory a natural physical mechanism to transform bosons into fermions (and vice versa).

Weyl invariance of the Green-Schwarz heterotic sigma model

Weyl invariance at one loop is proven for the heterotic non-linear sigma model coupled to curved superspace with non-trivial fermionic and bosonic background fields. A general formula is given relating the Weyl anomaly to the sigma model β-functions at arbitrary sigma-model loop order. The Weyl anomaly is also considered in the presence of Yang-Mills backgrounds.

On the conformal anomaly of the Green-Schwarz heterotic string in curved N=1, D=10 superspace

It is shown that the σ-model describing a Green-Schwarz heterotic string propagating in a curved N=1, D=10 superspace possesses a non-vanishing one loop world sheet conformal anomaly even when the background superfields satisfy their classical equations of motion. The anomaly is shown to disappear for a flat background superspace and for non-trivial bosonic background fields. We conjecture that the existence of this anomaly implies that it must cancel against an anomaly in the fermionic κ-symmetry (which must therefore exist) to preserve quantum consistency of the theory.

Loop-corrected string field equations from world-sheet Weyl invariance

We investigate short distance singularities inside the Polyakov path integral in an arbitrary closed bosonic string background due to vertex operators and small handles or holes. The latter are represented in terms of handle or hole operators, which we construct explicitly. The requirement of global Weyl invariance generates loop-corrected equations of motion for the string modes including tadpole terms and self-energy corrections. The relation to theS-matrix and superstrings are discussed briefly.

NUMERICAL SIMULATION OF THE HIGH-Tc SUPERCONDUCTORS

Monte Carlo simulations based on the Trotter-Suzuki transformation were carried out using 6 × 6 and 12 × 12 lattices and the single-band Hubbard model with intermediate-range repulsive interaction. The absence of the "minus-sign problem" for sufficiently low temperatures and appropriate doping indicates bosonic behavior reminiscent of superconductivity. It was found that holes prefer to pair on next-nearest-neighbor sites while nearest neighbors are suppressed. Additional electron-phonon coupling in the form of the breathing mode not only preserves this symmetry but strengthening of the bosonic background indicates the possibility of superconductivity.

Killing spinors and exact plane-wave solutions of extended supergravity

Urrutia's ansatz for exact plane-wave solutions of simple supergravity is generalized to $N=2$ extended supergravity and conditions are given for the solutions to be nontrivial. Conditions are also given for the plane-wave background to be invariant under a local supersymmetry transformation generated by a Killing spinor. It is seen that even though a bosonic background can admit a spin-$\frac{3}{2}$ solution when it does not possess a Killing spinor, if it is supersymmetric it admits a more general gravitino solution. Comparison is made with the solutions of Aichelburg and Dereli.