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Register a new userN=4 BPS black holes and octonionic twistors
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Authors
Yann Michel
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Stationary, spherically symmetric solutions of N=2 supergravity in 3+1 dimensions have been shown to correspond to holomorphic curves on the twistor space of the quaternionic-Kahler space which arises in the dimensional reduction along the time direction. In this note, we generalize this result to the case of 1/4-BPS black holes in N=4 supergravity, and show that they too can be lifted to holomorphic curves on a twistor space Z, obtained by fibering the Grassmannian F=SO(8)/U(4) over the moduli space in three-dimensions SO(8,n_v+2)/SO(8)xSO(n_v+2). This provides a kind of octonionic generalization of the standard constructions in quaternionic geometry, and may be useful for generalizing the known BPS black hole solutions, and finding new non-BPS extremal solutions.
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The motion of a particle near the Reissner-Nordstrom black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the N=4 superconformal mechanics coupled to n copies of N=8, d=1 vector supermultiplets. The constructed system possesses a special Kahler geometry in the scalar sector of the vector multiplets as well as an N=4 superconformal symmetry which is provided by a proper coupling to a dilaton superfield. The superconformal symmetry completely fixes the resulting action. We explicitly demonstrate that the electric and magnetic charges, presenting in the effective black hole action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the N=4 superconformal multiplet where its auxiliary components acquire non-zero constant values. We explicitly write down the corresponding modified black hole potential.
We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.
We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly known only up to three loops. Fortunately, the double coincidence limit of the four-loop integrals can be found by the method of expansion by regions, which reduces the problem of computing the four-point integrals to the evaluation of a large set of massless propagator integrals. These can in turn be evaluated by IBP reduction. The OPE limit of the stress tensor four-point function allows us to extract the (square of the) three-point couplings between two stress tensor multiplets and one twist two operator in the 20 of SU(4). The latest available IBP software accomplishes this task up to and including spin 8. With the data obtained we hope to further the development of the recent integrable systems picture for correlation functions.
The Hesse potential is constructed for a class of four-dimensional N=2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N=4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, $g_s$, and its complex conjugate. The terms depending holomorphically on $g_s$ are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of $g_s$ and $bar g_s$ are in principle present.
A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which develop anomalous dimensions in the quantum theory. The 1/4 BPS operators of the quantum theory are defined to be orthogonal to all the descendant operators with the same classical quantum numbers. It is shown, to order $g^2$, that these 1/4 BPS operators have protected dimensions.
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