# Altland, Zirnbauer ## Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures \[Links: [arXiv](https://arxiv.org/abs/cond-mat/9602137), [PDF](https://arxiv.org/pdf/cond-mat/9602137.pdf)\] \[Abstract: Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry classes are identified, which correspond to Cartan's symmetric spaces of type C, CI, D, and DIII. A detailed study is made of the systems where the phase shift due to Andreev reflection averages to zero along a typical semiclassical single-electron trajectory. Such systems are particularly interesting because they do not have a genuine excitation gap but support quasiparticle states close to the chemical potential. Disorder or dynamically generated chaos mixes the states and produces novel forms of universal level statistics. For two of the four universality classes, the n-level correlation functions are calculated by the mapping on a free 1D Fermi gas with a boundary. The remaining two classes are related to the Laguerre orthogonal and symplectic random-matrix ensembles. For a quantum dot with an NS-geometry, the weak localization correction to the conductance is calculated as a function of sticking probability and two perturbations breaking time-reversal symmetry and spin-rotation invariance. The universal conductance fluctuations are computed from a maximum-entropy S-matrix ensemble. They are larger by a factor of two than what is naively expected from the analogy with normal-conducting systems. This enhancement is explained by the doubling of the number of slow modes: owing to the coupling of particles and holes by the proximity to the superconductor, every cooperon and diffuson mode in the advanced-retarded channel entails a corresponding mode in the advanced-advanced (or retarded-retarded) channel.\] ## Summary - classification of [[0579 Random matrix theory|RMT]] # Banks, Fischler, Shenker, Susskind ## M Theory As A Matrix Model: A Conjecture \[Links: [arXiv](https://arxiv.org/abs/hep-th/9610043), [PDF](https://arxiv.org/pdf/hep-th/9610043.pdf)\] \[Abstract: We suggest and motivate a precise equivalence between uncompactified eleven dimensional [[0517 M-theory|M-theory]] and the $N = \infty$ limit of the supersymmetric matrix quantum mechanics describing [[0156 D-brane|D0-branes]]. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of [[0359 Supersymmetry|supersymmetry]] the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the [[0332 Supergravity|supergravity]] theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the [[0197 Matrix model|matrix model]]. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.\] # Chalmers, Siegel ## The self-dual sector of QCD amplitudes \[Links: [arXiv](https://arxiv.org/abs/hep-th/9606061), [PDF](https://arxiv.org/pdf/hep-th/9606061.pdf)\] \[Abstract: \] ## Refs - [[0136 Self-dual Yang-Mills]] # Duff, Liu, Rahmfeld ## Dipole Moments of Black Holes and String States \[Links: [arXiv](https://arxiv.org/abs/hep-th/9612015), [PDF](https://arxiv.org/pdf/hep-th/9612015.pdf)\] \[Abstract: As a further test of the conjectured equivalence of string states and extremal black holes, we compute the dipole moments of black holes with arbitrary spin and superspin in $D=4$, $N=4$ supergravity coupled to 22 vector multiplets and compare them with the dipole moments of states in the heterotic string on $T^6$ or the Type IIA string on $K3 \times T^2$. Starting from a purely bosonic black hole with Kerr angular momentum $L$, the superpartners are generated by acting with fermion zero modes, thus filling out the complete supermultiplet. $L$ is then identified with the superspin. On the heterotic side, elementary states belong only to short to long multiplets, but Type IIA elementary states can belong to intermediate multiplets as well. We find that the black hole gyromagnetic ratios are in perfect agreement with the string states not only for the BPS states belonging to short multiplets but also for those belonging to intermediate multiplets. In fact, these intermediate multiplets provide a stronger test of the black-hole/string-state equivalence because the gyromagnetic ratios are not determined by supersymmetry alone, in contrast to those of the short multiplets. We even find agreement between the non-supersymmetric (but still extremal) black holes and non-BPS string states belonging to long supermultiplets. In addition to magnetic dipole moments we also find electric dipole moments even for purely electrically charged black holes. The electric dipole moments of the corresponding string states have not yet been calculated directly but are consistent with heterotic/Type IIA duality.\] ## Comments - contains a discussion on getting black hole super-partners by doing a SUSY transformation on a bosonic solution with trivial fermions # Fatibene, Ferraris, Francaviglia, Godina (Aug) ## A geometric definition of Lie derivative for Spinor Fields \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9608003), [PDF](https://arxiv.org/pdf/gr-qc/9608003.pdf)\] \[Abstract: Relying on the general theory of Lie derivatives a new geometric definition of [[0527 Lie derivative of spinor fields|Lie derivative for general spinor fields]] is given, more general than Kosmann's one. It is shown that for particular infinitesimal lifts, i.e. for Kosmann vector fields, our definition coincides with the definition given by Kosmann more than 20 years ago.\] # Horowitz, Maldacena, Strominger ## Non-extremal BH microstates and U-duality \[Links: [arXiv](https://arxiv.org/abs/hep-th/9603109), [PDF](https://arxiv.org/pdf/hep-th/9603109.pdf)\] \[Abstract: \] ## Summary - *constructs* a six-parameter family of 5D BH solutions labelled by mass, two asymptotic scalar fields and three charges - *shows* that the Bekenstein-Hawking entropy is exactly matched by a duality-invariant extension of a formula for number of D-brane states in string theory ## Refs - contains a notion of pressure ## Matching between gravity and string theory - At strong coupling string theory reduces to gravity, while at weak coupling one can count string states more easily. For topological invariants, two calculations should agree although they reside at opposite regions, but more generally it is not necessarily true. - The black holes in this paper are uniquely decomposed into [[0156 D-brane]], anti-D-branes and strings, whose numbers are $\left(N_{1}, N_{\overline{1}}, N_{5}, N_{\overline{5}}, n_{R}, n_{L}\right)$. They are found by matching thermodynamic properties of BH to a collection of non-interacting D-branes and strings. # Marolf ## Path Integrals and Instantons in Quantum Gravity: Minisuperspace Models \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9602019), [PDF](https://arxiv.org/pdf/gr-qc/9602019.pdf)\] \[Abstract: \] ## Summary - use canonical formalism to derive a path integral for quantum [[0254 Minisuperspace]] models ## Finite dimensional reparameterisation invariant models - "Hamiltonian constraints" second order in momenta - reminiscent of WdW equations - neither Hamiltonian nor Euclidean action bounded below - just like Einstein gravity # Nunez, Quevedo, Sudarsky ## Black holes have no short hair \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9601020), [PDF](https://arxiv.org/pdf/gr-qc/9601020.pdf)\] \[Abstract: We show that in all theories in which black hole hair has been discovered, the region with non-trivial structure of the non-linear matter fields must extend beyond 3/2 the horizon radius, independently of all other parameters present in the theory. We argue that this is a universal lower bound that applies in every theory where hair is present. This *no short hair conjecture* is then put forward as a more modest alternative to the original *no hair conjecture*, the validity of which now seems doubtful.\] # Pradisi, Sagnotti, Stanev ## Completeness Conditions for Boundary Operators in 2D Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/hep-th/9603097), [PDF](https://arxiv.org/pdf/hep-th/9603097)\] \[Abstract: In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of [[1992#Lewellen|Lewellen]] on [[0602 Moore-Seiberg construction|sewing constraints]] for [[0548 Boundary CFT|conformal theories in the presence of boundaries]]. As a result, we include additional open sectors in the descendants of $D_{odd}$ $SU(2)$ WZW models. A new phenomenon emerges, the appearance of multiplicities and fixed-point ambiguities in the boundary algebra not inherited from the closed sector. We conclude by deriving a set of polynomial equations, similar to those satisfied by the fusion-rule coefficients $N_{ij}^k$, for a new tensor $A_{a b}^i$ that determines the open spectrum.\] # Strominger, Vafa ## Microscopic Origin of the Bekenstein-Hawking Entropy \[Links: [arXiv](https://arxiv.org/abs/hep-th/9601029), [PDF](https://arxiv.org/pdf/hep-th/9601029.pdf)\] \[Abstract: The [[0004 Black hole entropy|Bekenstein-Hawking area-entropy relation]] $S_{BH}=A/4$ is derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of [[0178 BPS|BPS]] soliton bound states.\] ## Charges - both the axion charge, $Q_H$, and electric charge, $Q_F$, are non-zero: otherwise get degenerate zero-area horizons ## Number of states - the log of number of states is computed to be $S_{s t a t}=2 \pi \sqrt{Q_H\left(\frac{1}{2} Q_F^2+1\right)}$ - this agrees with $A/4$ at large $Q_F$, which is $S_{B H}=2 \pi \sqrt{\frac{Q_H Q_F^2}{2}}$ ## Related topics - [[0248 Black hole microstates]] - [[0004 Black hole entropy]]