Axion-dilaton Field Research Articles

DS solutions with co-dimension 2 branes in six dimensions

We investigate phenomenological four-dimensional (4D) dS solutions with co-dimension 2 branes and finite 4D Planck mass in six dimensions. We present the conditions under which six-dimensional compactifications with holomorphic axion–dilaton field or models with pure gravity with local sources can yield 4D dS solutions. Different classes of solutions are specified by a holomorphic function describing different embeddings of multiple conical branes. Depending on the local singularities of this holomorphic function and the topology of the compact dimension, one has to introduce 3-branes creating a deficit angle equal to π and/or 4-branes with positive tensions.

Multi instanton tests of holography

Gauge theories living on stacks of D7-branes are holographically related to IIB gravitational backgrounds with a varying axion-dilaton field (F-theory). The axion-dilaton field is generated by D7, O7 and D-instanton sources and can be written in terms of the chiral correlators of the eight dimensional gauge theory living on the D7-branes. Using localization techniques, we prove that the same correlators determine the gauge coupling of the four-dimensional N=2 supersymmetric SU(2) gauge theories living on the elementary D3-brane which probes the F-theory geometries.

Q-instantons

We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is most conveniently described using the RR axion \chi and the dilaton \phi, the Q-instanton is most conveniently described using a different set of fields \chi' and T, where \chi' is an axionic scalar. The real part of the Q-instanton on-shell action is a function of T and the imaginary part is linear in \chi'. Discrete shifts of the axion \chi' correspond to PSL(2,Z) transformations that are of finite order. These are e.g. pure S-duality transformations relating weak and strongly coupled regimes. We argue that near each orbifold point of the quantum axion-dilaton moduli space PSL(2,Z)\PSL(2,R)/SO(2) the higher order R^4 terms in the string effective action contain contributions from an infinite sum of single multiply-charged instantons with the Q-instantons corresponding to the orbifold points \tau=i,\rho where \tau is the complex axion-dilaton field.

Half-BPS cosmic string in Script N = 2 supergravity in the presence of a dilaton

We construct new half-BPS cosmic string solutions in D=4 N=2 supergravity compatible with a consistent truncation to N=1 supergravity where they describe D-term cosmic strings. The constant Fayet-Iliopoulos term in the N=1 D-term is not put in by hand but is geometrically engineered by a gauging in the mother N=2 supergravity theory. The coupling of the N=2 vector multiplets is characterized by a cubic prepotential admitting an axion-dilaton field, a common property of many compactifications of string theory. The axion-dilaton field survives the truncation to N=1 supergravity. On the string configuration the BPS equations constrain the dilaton to be an arbitrary constant. All the cosmic string solutions with different values of the dilaton have the same energy per unit length but different lenght scales.

Symmetric space σ-model dynamics: Internal metric formalism

For the symmetric space sigma model in the internal metric formalism we explicitly construct the Lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion–dilaton field equations.

Entropy function for heterotic black holes

We use the entropy function formalism to study the effect of the Gauss-Bonnet term on the entropy of spherically symmetric extremal black holes in heterotic string theory in four dimensions. Surprisingly the resulting entropy and the near horizon metric, gauge field strengths and the axion-dilaton field are identical to those obtained by Cardoso et. al. for a supersymmetric version of the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet term. We also study the effect of holomorphic anomaly on the entropy using our formalism. Again the resulting attractor equations for the axion-dilaton field and the black hole entropy agree with the corresponding equations for the supersymmetric version of the theory. These results suggest that there might be a simpler description of supergravity with curvature squared terms in which we supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.

Bubbling 1/4 BPS solutions in type IIB and supergravity reductions on [formula omitted

We extend the construction of bubbling 1/2 BPS solutions of Lin, Lunin and Maldacena (H. Lin, O. Lunin, J. Maldacena, JHEP 0410 (2004) 025, hep-th/0409174) in two directions. First we enquire whether bubbling 1/2 BPS solutions can be constructed in minimal 6d supergravity and second we construct solutions that are 1/4 BPS in type IIB. We find that the S 1 × S 1 bosonic reduction of ( 1 , 0 ) 6d supergravity to 4d gravity coupled to 2 scalars and a gauge field is consistent only provided that the gauge field obeys a constraint ( F ∧ F = 0 ). This is to be contrasted to the case of the S 3 × S 3 bosonic reduction of type IIB supergravity to 4d gravity, 2 scalars and a gauge field, where consistency is achieved without imposing any such constraints. Therefore, in the case of ( 1 , 0 ) 6d supergravity we are able to construct 1/2 BPS solutions, similar to those derived in type IIB, provided that this additional constraint is satisfied. This ultimately prohibits the construction of a family of 1/2 BPS solutions corresponding to a bubbling AdS 3 × S 3 geometry. Returning to type IIB solutions, by turning on an axion–dilaton field we construct a family of bubbling 1/4 BPS solutions. This corresponds to the inclusion of back-reacted D7 branes to the solutions of Lin, Lunin and Maldacena.

General static spherically symmetric black holes of the heterotic string on a six-torus

We present the most general static, spherically symmetric solutions of the heterotic string compactified on a six-torus that conforms to the conjectured “no-hair theorem”, by performing a subset of O(8,24) transformations, i.e. symmetry transformations of the effective three-dimensional action for stationary solutions, on the Schwarzschild solution. The explicit form of the generating solution is determined by six SO(1,1) ⊂ O(8,24) boosts, with the zero Taub-NUT charge constraint imposing one constraint among two boost parameters. The non-nontrivial scalar fields are the axion-dilaton field and the moduli of the two-torus. The general solution, parameterized by unconstrained 28 magnetic and 28 electric charges and the ADM mass compatible with the Bogomol'nyi bound, is obtained by imposing on the generating solution [ SO(6) × SO(22)]/[ SO(4) × SO(20)] ⊂ O(6,22) ( T-duality) transformation and SO(2) ⊂ SL(2, R) (S- duality) transformation, which do not affect the four-dimensional space-time. Depending on the range of boost parameters, the non-extreme solutions have the space-time of either the Schwarzschild or the Reissner-Nordström black hole, while the extreme ones have either a null (or naked) singularity, or the space-time of the extreme Reissner-Nordström black hole.

Charge quantization of axion-dilaton black holes.

We present axion-dilaton black-hole and multi-black-hole solutions of the low-energy string effective action. Under $\mathrm{SL}(2, R)$ electric-magnetic duality rotations only the "hair" (charges and asymptotic values of the fields) of our solutions is transformed. The functional form of the solutions is duality invariant. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particlelike objects, which we call holons. We study the quantization of the charges of these objects and its compatibility with duality symmetry. In general the spectrum of black-hole solutions with quantized charges is not invariant under $\mathrm{SL}(2, R)$ but only under $\mathrm{SL}(2, Z)$ or one of its subgroups ${\ensuremath{\Gamma}}_{l}$. Because of their transformation properties, the asymptotic value of the axion-dilaton field of a black hole may be associated with the modular parameter $\ensuremath{\tau}$ of some complex torus and the integer numbers ($n, m$) that label its quantized electric and magnetic charges may be associated with winding numbers.