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Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3
Get PDFWe consider states with large angular momentum to facilitate the study of the M-theory regime of the AdS_4 /CFT_3 correspondence. More precisely, we study the duality between M-theory on AdS_4 × S^7/Z_k and N = 6 supersymmetric Chern–Simons-matter (ABJM) theory with gauge group U(N)×U(N) and level k, in the regime where k is of order one and N is large. In this regime the study of both sides of the duality is challenging: the lack of an explicit formulation of M-theory in AdS_4 × S^7/Z_k makes the gravity side difficult, while the CFT side is strongly coupled and the planar approximation is not applicable. In order to overcome these difficulties, we focus on states on the gravity side with large orbital angular momentum J ≫ 1 associated with a single plane of rotation in S^7 . We then identify the corresponding operators in the CFT, thereby establishing the AdS/CFT dictionary in this large angular momentum sector. We show that there are natural approximation schemes on both sides of the correspondence as a consequence of the presence of the small parameter 1/J. On the AdS side, the sector we focus on is well-approximated by the matrix model of M-theory – with matrices of size J/k – defined on the maximally supersymmetric eleven-dimensional pp-wave background. The pp-wave approximation to M-theory in AdS_4 × S^7/Z_k is justified for 1 ≪ J ≪ N^1/2 , while loop corrections in the matrix model are suppressed compared to tree-level contributions for J ≫ N^1/3 . On the CFT side, we study the ABJM theory defined on S^2 × R with large magnetic flux J/k. Using a carefully chosen gauge, we find an expansion of the Born–Oppenheimer type which arises naturally for large J in spite of the theory being strongly coupled. The energy spectra computed on the two sides agree at leading order. This provides a highly non-trivial test of the AdS_4 /CFT_3 correspondence including near-BPS observables associated with membrane degrees of freedom, therefore extending the validity of the AdS_4 /CFT_3 duality beyond the previously studied sectors corresponding to either BPS supergravity observables or the type IIA string regime
Critical behaviour of the fuzzy sphere
Get PDFWe study a multi-matrix model whose low temperature phase is a fuzzy sphere that undergoes an evaporation transition as the temperature is increased. We investigate finite size scaling of the system as the limiting temperature of stability of the fuzzy sphere phase is approached. We find on theoretical grounds that the system should obey scaling with specific heat exponent α = 1/2, shift exponent λ_bar = 4/3 and that the peak in the specific heat grows with exponent ω_bar = 2/3 . Using hybrid Monte Carlo simulations we find good collapse of specific heat data consistent with a scaling ansatz which give our best estimates for the scaling exponents as α = 0.50 ± 0.01, λ_bar = 1.41 ± 0.08 and ω_bar = 0.66 ± 0.08
Tadhg Ó Rodaighe and his school: aspects of patronage and poetic practice at the close of the bardic era
Get PDFAn examination of the phenomenon of the recycled poem, with reference to bardic poetry in the seventeenth century, and to the activities of a late school of poets in the Leitrim-Roscommon-Sligo area centred on the scribe and scholar, Tadhg Ó Rodaighe
Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes
Get PDFWe consider the thermodynamics of rotating and charged asymptotically de Sitter black holes. Using Hamiltonian perturbation theory techniques, we derive three different first law relations including variations in the cosmological constant, and associated Smarr formulas that are satisfied by such spacetimes. Each first law introduces a different thermodynamic volume conjugate to the cosmological constant. We examine the relation between these thermodynamic volumes and associated geometric volumes in a number of examples, including Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in D = 4. We also show that the Chong-Cvetic-Lu-Pope solution of D = 5 minimal supergravity, analytically continued to positive cosmological constant, describes black hole solutions of the Einstein-Chern-Simons theory and include such charged asymptotically de Sitter black holes in our analysis. In all these examples we find that the particular thermodynamic volume associated with the region between the black hole and cosmological horizons is equal to the naive geometric volume. Isoperimetric inequalities, which hold in the examples considered, are formulated for the different thermodynamic volumes and conjectured to remain valid for all asymptotically de Sitter black holes. In particular, in all examples considered, we find that for fixed volume of the observable universe, the entropy is increased by adding black holes. We conjecture that this is true in general
A novel (2+1)-dimensional model of chiral symmetry breaking
Get PDFWe propose a new model of flavour chiral symmetry breaking in a (2+1)-dimensional defect gauge theory of strongly coupled fermions by introducing probe D5/D5-flavour branes on the conifold. After working out the flavour brane embeddings at zero temperature, we thoroughly investigate the spectra of small fluctuations on the world volume of the flavour branes (meson spectra) and conclude that it is free of tachyons. Thus the proposed probe brane embedding is stable. Moreover, we introduce finite temperature and an external magnetic field and study the thermodynamics of the resulting configurations. Namely, we compute the free energies, entropies, heat capacities and magnetisations. The results are used to establish a detailed phase diagram of the model. We find that the effect of magnetic catalysis of chiral symmetry breaking is realised in our model and show that the meson-melting phase transition coincides with the chiral symmetry breaking phase transition. Furthermore, we show that the model is in a diamagnetic phase
"One glimpse of Ireland": the manuscript of Fr Nicolás (Fearghal Dubh) Ó Gadhra'
Get PDFA description and analysis of the Irish manuscript known as The Book of O'Gara (RIA MS 2 (23 F 16)), written in Lille and Brussels, 1655-9, by an Irish Augustinian, Fr Nicolás (Fearghal Dubh) Ó Gadhra. The paper also gives an account of the manuscript's history subsequent to its return to Ireland, particularly the addition to it of an address to the reader, composed, it is suggested, by Seaán Ó Gadhra
The ideal Bose gas in open harmonic trap systems and its condensation revisited
Get PDFWe rigorously revisit a textbook model used to figure out the Bose-Einstein condensation (BEC) phenomenon created by dilute cold alkali atoms gases in a magnetic-optical trap. It consists of a d-dimensional (d = 1, 2, 3) ideal non-relativistic spin-0 Bose gas confined in a box and trapped in an isotropic harmonic potential. Throughout we review and clarify a series of methods involved in the derivation of the thermodynamics in the grand-canonical situation. To make the derivation consistent with the usual rules of the statistical mechanics, we assign through our open-trap limit approach the role of canonical parameter to a rescaled number of particles (instead of an effective density involving the pulsation of the trap). Within this approach, we formulate an Einstein-like and Penrose-Onsager-like criterion of BEC and show their equivalence. Afterwards, we focus on the spatial localization of the condensate/thermal gas. When dealing with the reduced density matrix, our method is similar to the loop path approach
Comment on the higher derivative Lagrangians in relativistic theory
Get PDFWe discuss the consequences of higher derivative Lagrangians of the form (α_1)(A_μ)(x)ẋ^μ , (α_2)(G_μ)(x)ẍ^μ , · · · , U_((n)μ)(x)x^((n)μ) in relativistic theory. After establishing the equations of the motion of particles in these fields, we introduce the concept of the generalized induction principle assuming the coupling between the higher fields U_((n)μ)(x), n ≥ 1 with the higher currents j^(n)μ = ρ(x)x^(n)μ , where ρ(x) is the spatial density of mass or of electric charge. In addition, we discuss the analogy of the field G_μ(x) with the gravitational field and its inclusion in the general relativity framework in the last section. This letter is an invitation to reflect on a generalisation of the concept of inertia and we also discuss this problem in the last section
The compressibility of rotating black holes in D-dimensions
Get PDFTreating the cosmological constant as a pressure, in the context of black hole thermodynamics, a thermodynamic volume for the black hole can be defined as being the thermodynamic variable conjugate to the pressure, in the sense of a Legendre transform. The thermodynamic volume is explicitly calculated, as the Legendre transform of the pressure in the enthalpy, for a rotating asymptotically anti-de Sitter Myers-Perry black hole in D space-time dimensions. The volume obtained is shown to agree with previous calculations using the Smarr relation. The compressibility is calculated and shown to be non-negative and bounded.
Taking the limit of zero cosmological constant, the compressibility of a rotating black hole in asymptotically flat space-times is determined and the corresponding speed of sound computed. The latter is bounded above and has an elegant expression purely in terms of the angular momenta, in the form of quartic and quadratic Casimirs of the rotation group, SO(D − 1)