J. X. Lu

Phase transitions and critical behavior of black branes in canonical ensemble

We study the thermodynamics and phase structure of asymptotically flat nondilatonic as well as dilatonic black branes in a cavity in arbitrary dimensions (D). We consider the canonical ensemble and so the charge inside the cavity and the temperature at the wall are fixed. We analyze the stability of the black brane equilibrium states and derive the phase structures. For the zero charge case we find an analog of Hawking-Page phase transition for these black branes in arbitrary dimensions. When the charge is non-zero, we find that below a critical value of the charge, the phase diagram has a line of first-order phase transition in a certain range of temperatures which ends up at a second order phase transition point (critical point) as the charge attains the critical value. We calculate the critical exponents at that critical point. Although our discussion is mainly concerned with the non-dilatonic branes, we show how it easily carries over to the dilatonic branes as well.

The enriched phase structure of black branes in canonical ensemble

It is found that a necessary completion of phase structure of D-dimensional charged black p-brane (p>0) in a cavity requires two additional thermodynamical phases, the so-called “bubble of nothing” and/or the extremal brane, in canonical ensemble. This finding resolves the puzzle about the missing phases which are needed for the underlying phase diagram when d˜=D−p−3⩽2 and gives a new (bubble) phase which can become globally stable when d˜>2. An analog of Hawking–Page transition is also found among other new phase transitions, giving a complete phase structure in this setup.

A4 and CP symmetry and a model with maximal CP violation

Abstract We study a second CP symmetry compatible with the A 4 flavor group, which interchanges the representations 1 ′ and 1 ″ . We analyze the lepton mixing patterns arising from the A 4 and CP symmetry broken to residual subgroups Z 3 and Z 2 × C P in the charged lepton and neutrino sectors respectively. One phenomenologically viable mixing pattern is found, and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase, trivial Majorana phases and the correlation sin 2 ⁡ θ 12 cos 2 ⁡ θ 13 = 1 / 3 . We construct a concrete model based on the A 4 and CP symmetry, the above interesting mixing pattern is achieved, the observed charged lepton mass hierarchy is reproduced, and the reactor mixing angle θ 13 is of the correct order.

Phase structure of black branes in grand canonical ensemble

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black p-branes in a cavity in arbitrary dimensions D in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black p-branes is in some sense similar to that of the zero charge black p-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and ‘hot flat space’ is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black p-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black p-branes in D space-time dimensions.

Membrane duality revisited

Just as string T-duality originates from transforming field equations into Bianchi identities on the string worldsheet, so it has been suggested that M-theory U-dualities originate from transforming field equations into Bianchi identities on the membrane worldvolume. However, this encounters a problem unless the target space has dimension D=p+1. We identify the problem to be the nonintegrability of the U-duality transformation assigned to the pull-back map. Just as a double geometry renders manifest the O(D,D) string T-duality, here we show in the case of the M2-brane in D=3 that a generalized geometry renders manifest the SL(3)×SL(2) U-duality. In the case of M2-brane in D=4, with and without extra target space coordinates, we show that only the GL(4,R)⋉R4 subgroup of the expected SL(5,R) U-duality symmetry is realized.

Intersecting non-SUSY branes and closed string tachyon condensation

Abstract Following [H. Bai, J.X. Lu, S. Roy, Intersecting non-SUSY p -brane with chargeless 0-brane as black p -brane, JHEP 0701 (2007) 094, hep-th/0610264 ] we here consider the supergravity solutions representing the charged non-supersymmetric p -brane (for 1 ⩽ p ⩽ 6 ) intersecting with chargeless non-supersymmetric 1-brane and 0-brane of type II string theories. We show how these solutions nicely interpolate between black p -branes and the Kaluza–Klein “bubble of nothing” (BON) by continuously varying some parameters characterizing the solutions from one set of values to another. By performing a time symmetric general bubble initial data analysis, we show that the interpolation implies a possible transition from black p -branes to KK BON only for p ⩽ 4 , as in these cases there exist locally stable static bubbles under certain conditions. However, for p > 4 , black branes always decay into dynamical bubbles. Contrary to what is known in the literature, we argue that under certain conditions, the mechanism causing this transition to stable static bubbles can be the closed string tachyon condensation for all p ⩽ 4 . We also show that the configurations indeed contain (chargeless) F-strings required for the closed string tachyons to appear causing the transitions to occur.

The phase structure of black D1/D5 (F/NS5) system in canonical ensemble

A bstractIn this paper, we explore means which can be used to change qualitatively the phase structure of charged black systems. For this, we consider a system of black D1/D5 (or its S-dual F/NS5). We find that the delocalized charged black D-strings (F-strings) alone share the same phase structure as the charged black D5 branes (NS5-branes), having no van der Waals-Maxwell liquid-gas type. However, when the two are combined to form D1/D5 (F/NS5), the resulting phase diagram has been changed dramatically to a richer one, containing now the above liquid-gas type. The effect of adding the charged D-strings (F-strings) on the phase structure can also be effectively described as a slight increase of the transverse dimensions to the original D5 (NS5). This may be viewed as a connection between a brane charge and a fraction of spatial dimension at least in a thermodynamical sense.

The open string pair-production rate enhancement by a magnetic flux

We extend the amplitude calculations of [1] to exhaust the remaining cases for which one set of Dp branes carrying a flux (electric or magnetic) is placed parallel at separation to the other set carrying also a flux but with the two fluxes sharing at most one common field-strength index. We then find that the basic structure of amplitudes remains the same when the two fluxes share at least one common index but it is more general when the two fluxes share no common index. We discuss various properties of the amplitudes such as the large separation limit, the onset of various instabilities and the open string pair production. In particular, when one flux is electric and weak and the other is magnetic and fixed, we find that the open string pair production rate is greatly enhanced by the presence of this magnetic flux when the two fluxes share no common field-strength index and this rate becomes significant when the separation is on the order of string scale.

Modulating the phase structure of black D6 branes in canonical ensemble

A bstractThere exists a dramatic difference in phase structure between charged black Dp-branes with p < 5 and charged black D5 or D6 branes. In [1], we found that the phase structure of charged black D5 system can be changed qualitatively to that of charged black Dp with p < 5 by adding the delocalized D1 branes but the similar change does not happen for the charged black D6 system through adding the delocalized D2 branes (Note that both D1/D5 and D2/D6 belong to the same type of D(p - 4)/Dp system). Adding the delocalized D4 branes to the black D6 branes doesn’t work, either. In this paper, we consider adding the delocalized D0 branes, the only remaining lower dimensional branes, to the black D6 system for this purpose. We find that the delocalized charged black D0-branes alone share the same phase structure as the charged black D6 branes, having no van der Waals-Maxwell liquid-gas type. However, when the two are combined to form D0/D6, the resulting phase diagram finally gets changed dramatically to the wanted one, containing now the above liquid-gas type. This change arises from the interaction between D6 and the delocalized D0.

Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries

A bstractWe discussed the scenario that a discrete flavor group combined with CP symmetry is broken to Z2 × CP in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters θl and θν varying in the range of [0, π). As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group Δ(6n2) and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters θu and θd. A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group Δ(6n2) and CP, and accordingly the smallest value of the group index n is n = 7.