"Flip" of SL(2,R)-duality in five-dimensional supergravity

The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and the dimensionally reduced equations of motion have SL(2,R)/SO(2)-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in which the field equations have SL(2,R)/SO(1,1) invariance. In the timelike case, we develop a new duality transformation technique, while in the spacelike case we have done that in the previous work. As an example, by applying it to the Rasheed solutions, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. In general, in contrast to the spacelike case, the resulting dimensionally reduced solution includes the so-called NUT parameter and therefore from a four-dimensional point of view, such a spacetime is not asymptotically flat. However, it is shown that in some special cases, it can describe ordinary Kaluza-Klein black holes.Comment: 16 page

New approach to solution generation using SL(2,R)-duality of a dimensionally reduced space in five-dimensional minimal supergravity and new black holes

The dimensional reduction of (the bosonic sector of) five-dimensional minimal supergravity to four dimensions leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields (one of which has Chern-Simons coupling), whose field equations have SL(2,R)-invariance. Utilizing this SL(2,R)-duality, we provide a new formalism for solution generation. As an example, applying it to the Rasheed solution, which are known to describe dyonic rotating black holes (from the four-dimensional point of view) of five-dimensional pure gravity, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. We also show that the solutions have six charges: mass, angular momentum, Kaluza-Klein electric/magnetic charges and electric/magnetic charges of the Maxwell field, four of which are related by a constraint.Comment: 17 pages, a few references and comments added, to be published in PR

Little IIB Matrix Model

We study the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argue that the large N limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional spacetime. We also observe that it is due to non-gravitational interactions. We construct wave functions and vertex operators which realize the D=6, (2,0) tensor representation. We also comment on other "little" analogues of the IIB matrix model and Matrix Theory with less supercharges.Comment: 17 pages, references adde

3-dimensional Gravity from the Turaev-Viro Invariant

We study the $q$-deformed su(2) spin network as a 3-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines naturally regularized path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from the cosmological term is effectively included. The regularization dependent cosmological constant is found to be ${4\pi^2\over k^2} +O(k^{-4})$, where $q^{2k}=1$. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in 3-dimension.Comment: 11page

Chiral Generations on Intersecting 5-branes in Heterotic String Theory

We show that there exist two 27 and one 27 bar of E6, net one D=4, N=1 chiral matter supermultiplet as zero modes localized on the intersection of two 5-branes in the E8 x E8 heterotic string theory. The smeared intersecting 5-brane solution is used via the standard embedding to construct a heterotic background, which provides, after a compactification of some of the transverse dimensions, a five-dimensional Randall-Sundrum II like brane-world set-up in heterotic string theory. As a by-product, we present a new proof of anomaly cancellation between those from the chiral matter and the anomaly inflow onto the brane without small instanton.Comment: 26 pages, 5 figures; references added, typo correcte

On the stability of renormalizable expansions in three-dimensional gravity

Preliminary investigations are made for the stability of the $1/N$ expansion in three-dimensional gravity coupled to various matter fields, which are power-counting renormalizable. For unitary matters, a tachyonic pole appears in the spin-2 part of the leading graviton propagator, which implies the unstable flat space-time, unless the higher-derivative terms are introduced. As another possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1 part for any linear gauges in this case, but it can be removed if non-minimally coupled scalars are included. We suggest an interesting model which may be stable and possess an ultraviolet fixed point.Comment: 32 pages. (A further discussion to avoid tachyons is included. To be Published in Physical Review D.

The Geroch group in the Ashtekar formulation

We study the Geroch group in the framework of the Ashtekar formulation. In the case of the one-Killing-vector reduction, it turns out that the third column of the Ashtekar connection is essentially the gradient of the Ernst potential, which implies that the both quantities are based on the ``same'' complexification. In the two-Killing-vector reduction, we demonstrate Ehlers' and Matzner-Misner's SL(2,R) symmetries, respectively, by constructing two sets of canonical variables that realize either of the symmetries canonically, in terms of the Ashtekar variables. The conserved charges associated with these symmetries are explicitly obtained. We show that the gl(2,R) loop algebra constructed previously in the loop representation is not the Lie algebra of the Geroch group itself. We also point out that the recent argument on the equivalence to a chiral model is based on a gauge-choice which cannot be achieved generically.Comment: 40 pages, revte