Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nablaϕ)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order $e^{-1/g_3^2}$. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, as well as new predictions for higher genus perturbative contributions. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact $\nabla^2 F^4$ effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order $e^{-R}$ from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order $e^{-R^2}$ from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.
We give a proof of the recently proposed formula for the dyon spectrum in CHL string theories by mapping it to a configuration of D1 and D5-branes and Kaluza-Klein monopole. We also give a prescription for computing the degeneracy as a systematic expansion in inverse powers of charges. The computation can be formulated as a problem of extremizing a duality invariant statistical entropy function whose value at the extremum gives the logarithm of the degeneracy. During this analysis we also determine the locations of the zeroes and poles of the Siegel modular forms whose inverse give the dyon pa…
The degeneracies of supersymmetric quarter BPS dyons in four dimensions and of spinning black holes in five dimensions in a CHL compactification are computed exactly using Borcherds lift. The Hodge anomaly in the construction has a physical interpretation as the contribution of a single M-theory Kaluza-Klein 6-brane in the 4d-5d lift. Using factorization, it is shown that the resulting formula has a natural interpretation as a two-loop partition function of left-moving heterotic string, consistent with the heuristic picture of dyons in the M-theory lift of string webs.
We compute the genus-two chiral partition function of the left-moving heterotic string for a $\mathbb{Z}_2$ CHL orbifold. The required twisted determinants can be evaluated explicitly in terms of the untwisted determinants and theta functions using orbifold techniques. The dependence on Prym periods cancels neatly once summation over odd charges is properly taken into account. The resulting partition function is a Siegel modular form of level two and precisely equals recently proposed dyon partition function for this model. This result provides an independent weak coupling derivation of the dy…
The original proposal of Dijkgraaf, Verlinde and Verlinde for the quarter BPS dyon partition function in heterotic string theory on T^6 is known to correctly produce the degeneracy of dyons of torsion 1, i.e. dyons for which gcd(Q\wedge P)=1. We propose a generalization of this formula for dyons of arbitrary torsion. Our proposal satisfies the constraints coming from S-duality invariance, wall crossing formula, black hole entropy and the gauge theory limit. Furthermore using our proposal we derive a general wall crossing formula that is valid even when both the decay products are non-primitive…
For heterotic string theory compactified on T^6, we derive the complete set of T-duality invariants which characterize a pair of charge vectors (Q,P) labelling the electric and magnetic charges of the dyon. Using this we can identify the complete set of dyons to which the previously derived degeneracy formula can be extended. By going near special points in the moduli space of the theory we derive the spectrum of quarter BPS dyons in N=4 supersymmetric gauge theory with simply laced gauge groups. The results are in agreement with those derived from field theory analysis.
We study a class of rotating dyonic black holes in the heterotic string theory in four dimension which have left, right independent electric charges but have same magnitude for the left and right magnetic charges. In both left and right sector the electric and the magnetic vectors are orthogonal to each other. The gyromagnetic(electric) ratios are in general found not to have an upper bound.
We present a few remarks on disconnected components of the moduli space of heterotic string compactifications on $T_2$. We show in particular how the eight dimensional CHL heterotic string can be understood in terms of topologically non-trivial $E_8\times E_8$ and $\Spin(32)/Z_2$ vector bundles over the torus, and that the respective moduli spaces coincide.
The static Yang-Mills-Higgs dyonic instanton is shown to have a non-vanishing, but anti-self-dual, angular momentum 2-form with skew eigenvalues equal to the electric charge; for large charge the angular momentum causes the instanton to expand into a hyper-spherical shell. A class of exact multi dyonic instantons is then found and then generalized to a new class of 1/4 supersymmetric, non-singular, stationary, exact solutions of the ten-dimensional supergravity/Yang-Mills theory. These self-gravitating dyonic instantons yield new heterotic string solitons, to leading order in the inverse strin…
We revisit our earlier work which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS (dyons) in $\mathcal{N}=4$ supersymmetric four-dimensional string theory. We make new additions to the periodic table by making use of connections with generalized Mathieu moonshine as well as umbral moonshine. We show the modularity of some Siegel modular forms that appear in umbral moonshine associated with Niemeier lattices constructed from A-type root systems and further show that the same Siegel modular forms appear for g…
We study some features of dyonic Black hole solution in heterotic string theory on a six torus. This solution has 58 parameters. Of these, 28 parameters denote the electric charge of the black hole, another 28 correspond to the magnetic charge, and the other two parameters being the mass and the angular momentum of the black hole. We discuss the extremal limit and show that in various limits, it reduces to the known black hole solutions. The solutions saturating the Bogomolnyi bound are identified. Explicit solution is presented for the non-rotating dyonic black hole.
Motivated by recent advances in Donaldson-Thomas theory, four-dimensional $\mathcal{N}=4$ string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of "untwisted" quarter-BPS dyons in the heterotic $\mathbb{Z}_2$ CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup $B(2) \subset \text{Sp}_4 (\mathbb{Z}) $ which generate BPS indices for dyons w…
Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form $F(Φ) (\nablaΦ)^4$ in a class of string vacua known as CHL $\mathbb{Z}_N$ heterotic orbifolds with $N$ prime, generalizing our previous work which dealt with the case of heterotic string on $T^6$. We derive the Ward identities that $F(Φ)$ must satisfy, and check that our formula obeys them. We analyze the weak coupling ex…
We propose a formula for the degeneracy of quarter BPS dyons in a class of CHL models. The formula uses a modular form of a subgroup of the genus two modular group Sp(2,Z). Our proposal is S-duality invariant and reproduces correctly the entropy of a dyonic black hole to first non-leading order for large values of the charges.
All the linear alpha-prime corrections, however excluding the gravitational Chern-Simons correction, are studied in the toroidally compactified critical Heterotic string theory. These corrections are computed to the entropy for a BPS static spherical four dimensional dyonic black hole which represents a wrapped fundamental string carrying arbitrary winding and momentum charges along one cycle in the presence of KK-monopole and H-monopole charges associated to another cycle. It is verified that after the inclusion of the gravitational Chern-Simons corrections [hep-th/0608182], all the linear al…
Heterotic strings on $R^6 \times K3$ generically appear to undergo some interesting new phase transition at that value of the string coupling for which the one of the six-dimensional gauge field kinetic energies changes sign. An exception is the $E_8 \times E_8$ string with equal instanton numbers in the two $E_8$'s, which admits a heterotic/heterotic self-duality. In this paper, we generalize the dyonic string solution of the six-dimensional heterotic string to include non-trivial gauge field configurations corresponding to self-dual Yang-Mills instantons in the four transverse dimensions. We…
A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,Z). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,Z) group.
We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in $4D$ $\mathcal{N} =4$ heterotic $\mathbb{Z}_N$ CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models.
We explicitly compute the entropy of an extremal dyonic black hole in heterotic string theory compactified on T^6 or K3\times T^2 by taking into account all the tree level four derivative corrections to the low energy effective action. For supersymmetric black holes the result agrees with the answer obtained earlier 1) by including only the Gauss-Bonnet corrections to the effective action 2) by including all terms related to the curvature squared terms via space-time supersymmetry transformation, and 3) by using general arguments based on the assumption of AdS_3 near horizon geometry and space…
We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is given in terms of Siegel modular forms associated with genus-two Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance of the resulting degeneracies and give a prescription that makes the invariance manifest. We show, using M-theory lift of string webs, that the genus-two contribution captures the degeneracy only if a specific irreduci…
We study ${\cal N}=2$ compactifications of heterotic string theory on the CHL orbifold $(K3\times T^2)/\mathbb{Z}_N$ with $N= 2, 3, 5, 7$. $\mathbb{Z}_N$ acts as an involution on $K3$ together with a shift of $1/N$ along one of the circles of $T^2$. These compactifications generalize the example of the heterotic string on $K3\times T^2$ studied in the context of dualities in ${\cal N}=2$ string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can written in terms of the McKay-Thompson series associated with the $\mathbb{Z}_N$ involution embedd…
Families of exact $(0,2)$ supersymmetric conformal field theories of magnetically and electrically charged extremal 4D black hole solutions of heterotic string theory are presented. They are constructed using a $(0,1)$ supersymmetric $SL(2,R)\times SU(2)$ WZW model where anomalously embedded $U(1)\times U(1)$ subgroups are gauged. Crucial cancelations of the $U(1)$ anomalies coming from the supersymmetric fermions, the current algebra fermions and the gauging ensure that there is a consistency of these models at the quantum level. Various 2D models, which may be considered as building blocks f…
Within effective heterotic superstring theory compactified on a six-torus we derive minimum energy (supersymmetric), static, spherically symmetric solutions, which are manifestly invariant under the target space $O(6,22)$ and the strong-weak coupling $SL(2)$ duality symmetries with 28 electric and 28 magnetic charges subject to one constraint. The class of solutions with a constant axion corresponds to dyonic configurations subject to two charge constraints, with purely electric [or purely magnetic] and dyonic configurations preserving ${1\over 2}$ and ${1\over 4}$ of $N=4$ supersymmetry, resp…
Starting with the Taub--NUT solution to Einstein's equations, together with a constant dilaton, a dyonic Taub--NUT solution of low energy heterotic string theory with non--trivial dilaton, axion and $U(1)$ gauge fields is constructed by employing $O(1,1)$ transformations. The electromagnetic dual of this solution is constructed, using $SL(2,\rline)$ transformations. By an appropriate change to scaled variables, the extremal limit of the dual solution is shown to correspond to the low energy limit of an exact conformal field theory presented previously.
We calculate alpha'^2-corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R^2-correction obtained by…
We propose a general set of constraints on the partition function of quarter BPS dyons in any N=4 supersymmetric string theory by drawing insight from known examples, and study the consequences of this proposal. The main ingredients of our analysis are duality symmetries, wall crossing formula and black hole entropy. We use our analysis to constrain the dyon partition function for two hitherto unknown cases -- the partition function of dyons of torsion two (i.e. gcd(Q\wedge P)=2) in heterotic string theory on T^6 and the partition function of dyons carrying untwisted sector electric charge in …
We define a very general class of CHL-models associated with any string theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We take the orbifold by a pair (g,δ), where g is a (possibly non-geometric) symmetry of C and δis a translation along T^d. We analyze the T-dualities of these models and show that in general they contain Atkin-Lehner type symmetries. This generalizes our previous work on N=4 CHL-models based on heterotic string theory on T^6 or type II on K3 x T^2, as well as the `monstrous' CHL-models based on a compactification of heterotic string theory on the F…
We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a…
Within a four-dimensional, toroidally compactified heterotic string, we identify (quantized) charge vectors of electrically charged BPS-saturated states (along with the tower of SL(2,Z) related dyonic states), which preserve 1/2 of N=4 supersymmetry and become massless along the hyper-surfaces of enhanced gauge symmetry of the two-torus moduli sub-space. In addition, we identify charge vectors of the dyonic BPS-saturated states (along with the tower of SL(2,Z) related states), which preserve 1/4 of N=4 supersymmetry, and become massless at two points with the maximal gauge symmetry enhancement…
We present a relatively simple argument showing that the H-dyon states required by S-duality of the heterotic string on $T^6$ are present provided that the BPS dyons required by S-duality of N=4 supersymmetric Yang-Mills theory are present. We also conjecture and provide evidence that H-dyons at singularities where the nonperturbative gauge symmetry is completely broken are actually BPS dyons.
We discuss an orbifold of the toroidally compactified heterotic string which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry. This construction yields the moduli space of the first of a series of reduced rank theories with maximal supersymmetry discovered recently by Chaudhuri, Hockney, and Lykken. Such moduli spaces contain non-simply-laced enhanced symmetry points in any spacetime dimension D<10. Precisely in D=4 the set of allowed gauge groups is invariant under electric-magnetic duality, providing further evidence for S-duality of the D=4 he…
We derive the wall crossing formula for the decay of a quarter BPS dyon into a pair of half-BPS dyons by analyzing the quantum dynamics of multi-centered black holes in N=4 supersymmetric string theories. Our analysis encompasses the cases where the final decay products are non-primitive dyons. The results are in agreement with the microscopic formula for the dyon spectrum in the special case of heterotic string theory on T^6.
Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the …
Dyonic black holes with string-loop corrections are studied in the near-horizon region. In perturbative heterotic string theory compactified to four dimensions with N=2 supersymmetry, in the first order in string-loop expansion parameter, we solve the system of Maxwell and Killing spinor equations for dyonic black hole. At the horizon, the string-loop-corrected solution displays restoration of spontaneously broken supersymmetry.
The spherical symmetric dyonic black hole solutions of the effective action of heterotic string are studied perturbatively up to second order in the inverse string tension. An expression for the temperature in term of the mass and the electric and magnetic charge of the black hole is derived and it is shown that its behaviour is qualitatively different in the two special cases where either the electric or the magnetic charge vanishes
We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) action…
Using dyonic solutions in the type IIA superstring theory on Calabi-Yau manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BH) and black 2-branes (B2B) carrying 8 electric charges and 8 magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on T^{4} to four-qubit states. These states are interpreted…
We show that the generating function of electrically charged 1/2-BPS states in N=4 supersymmetric Z_N-CHL orbifolds of the heterotic string on T^6 are given by multiplicative eta-products. The eta-products are determined by the cycle shape of the corresponding symplectic involution in the dual type II picture. This enables us to complete the construction of the genus-two Siegel modular forms due to David, Jatkar and Sen [arXiv:hep-th/0609109] for Z_N orbifolds when N is non-prime. We study the Z_4 CHL orbifold in detail and show that the associated Siegel modular forms, Φ_3(Z) and \widetildeΦ_…
We propose a candidate for the dual (in the weak/strong coupling sense) of the six-dimensional heterotic string compactification constructed recently by Chaudhuri, Hockney and Lykken. It is a type IIA string theory compactified on an orbifold $K3/Z_2$, where the $Z_2$ action involves an involution of $K3$ with fixed points, and also has an embedding in the U(1) gauge group associated with the Ramond-Ramond sector of the type IIA string theory. This introduces flux of the U(1) gauge field concentrated at the orbifold points. This construction provides an explicit example where the dual of a sup…
The known BPS dyon black hole solutions of the N=4 heterotic string in four dimensions with non-zero angular momentum all have naked singularities. We show that it is possible to modify a certain class of these solutions by the addition of massive Kaluza-Klein fields in such a way that the solutions decompactify near the core to five-dimensional black hole solutions with regular event horizons. We argue that the degeneracy of the four-dimensional BPS dyon states is given, for large charges, by the five-dimensional geometric entropy.
CHL compactifications are supersymmetry preserving orbifolds of any perturbatively renormalizable and ultraviolet finite ground state of the perturbative string theories: heterotic, type I, or type II, preserving 32, 16, 12, 8, 4, (or zero) supersymmetries, and retaining the perturbative renormalizability and finiteness of the parent string vacuum. In this paper, we review the genesis of the CHL (Chaudhuri-Hockney-Lykken) project within the broader context of the full String/M Duality web, establishing the existence of moduli spaces with a small number of massless scalar fields, the decompacti…
In heterotic string theory compactified to four dimensions with N=2 supersymmetry, string-loop corrections to the universal sector of the low-energy effective action are studied. Within the framework of N=2 supersymmetric formulation of the theory, in the first order in string coupling constant, we solve the system of the loop-corrected Maxwell and Killing spinor equations. Taking as the in-put the tree-level dyonic black hole solution, we calculate string-loop corrections to the string tree-level metric and moduli of dyonic black hole.
We study the degeneracy of quarter BPS dyons in N =4 type II compactifications of string theory. We find that the genus-two Siegel modular forms generating the degeneracies of the quarter BPS dyons in the type II theories can be expressed in terms of the genus-two Siegel modular forms generating the degeneracies of quarter BPS dyons in the CHL theories and the heterotic string. This helps us in understanding the algebra structure underlying the degeneracy of the quarter BPS states. The Conway group, Co_1, plays a role similar to Mathieu group, M_{24}, in the CHL models with eta quotients appea…
We address non-perturbative effects and duality symmetries in $N=2$ heterotic string theories in four dimensions. Specifically, we consider how each of the four lines of enhanced gauge symmetries in the perturbative moduli space of $N=2$ $T_2$ compactifications is split into 2 lines where monopoles and dyons become massless. This amounts to considering non-perturbative effects originating from enhanced gauge symmetries at the microscopic string level. We show that the perturbative and non-perturbative monodromies consistently lead to the results of Seiberg-Witten upon identication of a consist…
We consider Euclidean SU(N) Yang-Mills theory on the space GxR, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G=SU(2)=S^3, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on GxR to Minkowski and construct f…
We consider a six-dimensional solitonic string solution described by a conformal chiral null model with non-trivial $N=4$ superconformal transverse part. It can be interpreted as a five-dimensional dyonic solitonic string wound around a compact fifth dimension. The conformal model is regular with the short-distance (`throat') region equivalent to a WZW theory. At distances larger than the compactification scale the solitonic string reduces to a dyonic static spherically-symmetric black hole of toroidally compactified heterotic string. The new four-dimensional solution is parameterised by five …
We determine the generating functions of 1/4 BPS dyons in a class of 4d $\mathcal{N}=4$ string vacua arising as CHL orbifolds of $K3 \times T^2$, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be…
In this letter, we investigate corrections to quartic gauge couplings in compactifications of string theories on a 2-torus without vector structure. First, we calculate the threshold corrections to F^4 terms in the heterotic CHL string. Then, using the CHL string/type I duality dictionary, we map these corrections to perturbative and non-perturbative effects in type I string compactified on 2-torus without vector structure. Comparing the perturbative terms provides a quantitative test of the S-duality conjecture. The non-perturbative contributions are due to D-strings wrapping the torus. A T-d…
It is shown that all the (p,q) dyon bound states exist and are unique in N=4 and N=2 with four massless flavours supersymmetric SU(2) Yang-Mills theories, where p and q are any relatively prime integers. The proof can be understood in the context of field theory alone, and does not rely on any duality assumption. We also give a general physical argument showing that these theories should have at least an exact Gamma(2) duality symmetry, and then deduce in particular the existence of the (2p,2q) vector multiplets in the Nf=4 theory. The corresponding massive theories are studied in parallel, an…
Classical single centered solutions of $1/4$ BPS dyons in ${\cal N}=4$ theories are usually constructed in duality frames which contain non-trivial hair degrees of freedom localized outside the horizon. These modes are in addition to the fermionic zero modes associated with broken supersymmetry. Identifying and removing the hair from the $1/4$ BPS index allows us to isolate the degrees of freedom associated with the horizon. The spherical symmetry of the horizon then ensures that index of the horizon states has to be positive. We verify that this is indeed the case for the canonical example of…
We study three properties of $1/4$ BPS dyons at small charges in string compactifications which preserve ${\cal N}=4$ supersymmetry. We evaluate the non-trivial constant present in the one loop statistical entropy for ${\cal N}=4$ compactifications of type IIB theory on $K3\times T^2$ orbifolded by an order $\mathbb{Z}_N$ freely acting orbifold $g'$ including all CHL compactifications. This constant is trivial for the un-orbifolded model but we show that it contributes crucially to the entropy of low charge dyons in all the orbifold models. We then show that the meromorphic Jacobi form which c…
A class of four-dimensional static supersymmetric black hole solutions of effective supergravity Lagrangian of IIA superstring compactified on $T^6$ is constructed by explicitly solving Killing spinor equations (KSEs). These solutions are dyonic black holes parametrized by four charges, with dilaton and diagonal internal metric components as the only non-zero scalar fields, and preserve $1 \over 8$ of $N=8$ supersymmetry. The KSEs with only Neveu-Schwarz-Neveu-Schwarz charges relate spinors with opposite chirality from ten-dimensional view point, and have identical structures with KSEs of toro…
We show that a four-parameter generating solution for a general class of four-dimensional, spherically-symmetric, static, dyonic BPS saturated solutions of leading-order effective equations of toroidally compactified heterotic or type II superstring theory are exact string solutions. The corresponding ten-dimensional background defines a conformal sigma-model which is a particular case of a `chiral null model' with curved `transverse' part. The exact conformal invariance is a consequence of the chiral null structure of the `electric' part of the model and the N=4 world-sheet supersymmetry of i…
Supersymmetric extreme dyonic black holes of toroidally compactified heterotic or type II string theory can be viewed as lower-dimensional images of solitonic strings wound around a compact dimension. We consider conformal sigma models which describe string configurations corresponding to various extreme dyonic black holes in four and five dimensions. These conformal models have regular short-distance region equivalent to a WZW theory with level proportional to magnetic charges. Arguments are presented suggesting a universal relation between the black hole entropy (area) and the statistical en…
We apply the duality transformation relating the heterotic to the IIA string in 6D to the class of exact string solutions described by the chiral null model and derive explicit formulas for all fields after reduction to 4D. If the model is restricted to asymptotically flat black hole type solutions with well defined mass and charges the purely electric solutions on the heterotic side are mapped to dyonic ones on the IIA side. The mass remains invariant. Before and after the duality transformation the solutions belong to short $N=4$ SUSY multiplets and saturate the corresponding Bogomol'nyi bou…
The microscopic spectrum of half-BPS excitations in toroidally compactified heterotic string theory has been computed exactly through the use of results from analytic number theory. Recently, similar quantities have been understood macroscopically by evaluating the gravitational path integral on the M-theory lift of the AdS2 near-horizon geometry of the corresponding black hole. In this paper, we generalize these results to a subset of the CHL models, which include the standard compactification of IIA on $K3\times T^2$ as a special case. We begin by developing a Rademacher-like expansion for t…
