223 research outputs found
Decoupling limits of N=4 super Yang-Mills on R x S^3
We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with
gauge group SU(N). These decoupling limits lead to decoupled theories that are
much simpler than the full N=4 SYM but still contain many of its interesting
features. The decoupling limits correspond to being in a near-critical region,
near a point with zero temperature and critical chemical potentials. The new
decoupling limits are found by generalizing the limits of hep-th/0605234 to
include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM
but also the chemical potentials corresponding to the SO(4) symmetry. In the
decoupled theories it is possible to take a strong coupling limit in a
controllable manner since the full effective Hamiltonian is known. For planar
N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable
spin chains. We study the thermodynamics of the decoupled theories and find the
Hagedorn temperature for small and large values of the effective coupling. We
find an alternative formulation of the decoupling limits in the microcanonical
ensemble. This leads to a characterization of certain regimes of weakly coupled
N=4 SYM in which there are string-like states. Finally, we find a similar
decoupling limit for pure Yang-Mills theory, which for the planar limit leads
to a fully integrable decoupled theory.Comment: 48 pages, 1 figure; added references, published versio
Thermodynamics of Squashed Kaluza-Klein Black Holes and Black Strings -- A Comparison of Reference Backgrounds --
We investigate thermodynamics constructed on different background reference
spacetimes for squashed Kaluza-Klein (SqKK) black hole and electrically charged
black string in five-dimensional Einstein-Maxwell system. Two spacetimes are
possible to be reference spacetimes giving finite gravitational classical
actions: one is four-dimensional Minkowski times a circle and the other is the
KK monopole. The boundary of the SqKK black hole can not be matched perfectly
to that of the former reference spacetime because of the difference in
topology. However, the resultant classical action coincides with that
calculated by the counterterm subtraction scheme. The boundary of the KK
monopole has the same topology with that of the SqKK black hole and can be
matched to the boundary of the black hole perfectly. The resultant action takes
different value from the result given by using the former reference spacetime.
After a brief review of thermodynamic quantities of the black hole solutions,
we calculate thermodynamic potentials relevant for several thermodynamic
environments. The most stable state is different for each environment: For
example, the KK monopole is the most stable state in isothermal environment
with fixed gravitational tension. On the other hand, when the size of the
extra-dimension is fixed, the Minkowski times a circle is the most stable. It
is shown that these two spacetimes can be reference spacetimes of the
five-dimensional black string.Comment: 28 pages; references added, typo corrected;version accepted for
publication in Class. Quantum Gra
On non-uniform smeared black branes
We investigate charged dilatonic black -branes smeared on a transverse
circle. The system can be reduced to neutral vacuum black branes, and we
perform static perturbations for the reduced system to construct non-uniform
solutions. At each order a single master equation is derived, and the
Gregory-Laflamme critical wavelength is determined. Based on the non-uniform
solutions, we discuss thermodynamic properties of this system and argue that in
a microcanonical ensemble the non-uniform smeared branes are entropically
disfavored even near the extremality, if the spacetime dimension is , which is the critical dimension for the vacuum case. However, the critical
dimension is not universal. In a canonical ensemble the vacuum non-uniform
black branes are thermodynamically favorable at , whereas the
non-uniform smeared branes are favorable at near the extremality.Comment: 24 pages, 2 figures; v2: typos corrected, submitted to
Class.Quant.Gra
Formation of Five-Dimensional String Solutions from the Gravitational Collapse
We study the formation of five-dimensional string solutions including the
Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the
geometry with a naked singularity from the gravitational collapse. The interior
solutions of five-dimensional Einstein equations describe collapsing
non-isotropic matter clouds. It is shown that the matter cloud always forms the
GL black string solution while the KK bubble solution cannot be formed. The
numerical study seems to suggest that the collapsing matter forms the
geometries with timelike naked curvature singularities, which should be taken
cautiously as the general relativity is not reliable in the strong curvature
regime.Comment: 17 pages, 10 figures, LaTeX, to appear in Class. Quant. Grav., a
appendix and some discussions added, title change
New Phase Diagram for Black Holes and Strings on Cylinders
We introduce a novel type of phase diagram for black holes and black strings
on cylinders. The phase diagram involves a new asymptotic quantity called the
relative binding energy. We plot the uniform string and the non-uniform string
solutions in this new phase diagram using data of Wiseman. Intersection rules
for branches of solutions in the phase diagram are deduced from a new Smarr
formula that we derive.Comment: 19 pages, 6 figures, v2: typos corrected, v3: refs. added, comment on
bounds on the relative binding energy n added in end of section
Phase structure of matrix quantum mechanics at finite temperature
We study matrix quantum mechanics at finite temperature by Monte Carlo
simulation. The model is obtained by dimensionally reducing 10d U(N) pure
Yang-Mills theory to 1d. Following Aharony et al., one can view the same model
as describing the high temperature regime of (1+1)d U(N) super Yang-Mills
theory on a circle. In this interpretation an analog of the deconfinement
transition was conjectured to be a continuation of the black-hole/black-string
transition in the dual gravity theory. Our detailed analysis in the critical
regime up to N=32 suggests the existence of the non-uniform phase, in which the
eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The
transition to the gapped phase is of second order. The internal energy is
constant (giving the ground state energy) in the uniform phase, and rises
quadratically in the non-uniform phase, which implies that the transition
between these two phases is of third order.Comment: 17 pages, 9 figures, (v2) refined arguments in section 3 ; reference
adde
Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
In order to understand thermodynamical properties of N D-branes with chemical
potentials associated with R-symmetry charges, we study a one dimensional large
N gauge theory (bosonic BFSS type model) as a first step. This model is
obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills
theory and we use a 1/D expansion to investigate the phase structure. We find
three phases in the \mu-T plane. We also show that all the adjoint scalars
condense at large D and obtain a mass dynamically. This dynamical mass protects
our model from the usual perturbative instability of massless scalars in a
non-zero chemical potential. We find that the system is at least meta-stable
for arbitrary large values of the chemical potentials in D \to \infty limit. We
also explore the existence of similar condensation in higher dimensional gauge
theories in a high temperature limit. In 2 and 3 dimensions, the condensation
always happens as in one dimensional case. On the other hand, if the dimension
is higher than 4, there is a critical chemical potential and the condensation
happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3:
minor corrections, to appear in JHE
Phases of Thermal N=2 Quiver Gauge Theories
We consider large N U(N)^M thermal N=2 quiver gauge theories on S^1 x S^3. We
obtain a phase diagram of the theory with R-symmetry chemical potentials,
separating a low-temperature/high-chemical potential region from a
high-temperature/low-chemical potential region. In close analogy with the N=4
SYM case, the free energy is of order O(1) in the low-temperature region and of
order O(N^2 M) in the high-temperature phase. We conclude that the N=2 theory
undergoes a first order Hagedorn phase transition at the curve in the phase
diagram separating these two regions. We observe that in the region of zero
temperature and critical chemical potential the Hilbert space of gauge
invariant operators truncates to smaller subsectors. We compute a l-loop
effective potential with non-zero VEV's for the scalar fields in a sector where
the VEV's are homogeneous and mutually commuting. At low temperatures the
eigenvalues of these VEV's are distributed uniformly over an S^5/Z_M which we
interpret as the emergence of the S^5/Z_M factor of the holographically dual
geometry AdS_5 x S^5/Z_M. Above the Hagedorn transition the eigenvalue
distribution of the Polyakov loop opens a gap, resulting in the collapse of the
joint eigenvalue distribution from S^5/Z_M x S^1 into S^6/Z_M.Comment: 40 pages text + 15 pages appendix, 3 figures, latex; v2: one minor
typo corrected and typeset in JHEP format; v3: computation of saddle points
in Sec. 4.2 improved, discussion of stability of saddle points added in Sec.
6.2, minor changes, ref. adde
New Horizons for Black Holes and Branes
We initiate a systematic scan of the landscape of black holes in any
spacetime dimension using the recently proposed blackfold effective worldvolume
theory. We focus primarily on asymptotically flat stationary vacuum solutions,
where we uncover large classes of new black holes. These include helical black
strings and black rings, black odd-spheres, for which the horizon is a product
of a large and a small sphere, and non-uniform black cylinders. More exotic
possibilities are also outlined. The blackfold description recovers correctly
the ultraspinning Myers-Perry black holes as ellipsoidal even-ball
configurations where the velocity field approaches the speed of light at the
boundary of the ball. Helical black ring solutions provide the first instance
of asymptotically flat black holes in more than four dimensions with a single
spatial U(1) isometry. They also imply infinite rational non-uniqueness in
ultraspinning regimes, where they maximize the entropy among all stationary
single-horizon solutions. Moreover, static blackfolds are possible with the
geometry of minimal surfaces. The absence of compact embedded minimal surfaces
in Euclidean space is consistent with the uniqueness theorem of static black
holes.Comment: 54 pages, 7 figures; v2 added references, added comments in the
subsection discussing the physical properties of helical black rings; v3
added references, fixed minor typo
Black Holes in Higher-Dimensional Gravity
These lectures review some of the recent progress in uncovering the phase
structure of black hole solutions in higher-dimensional vacuum Einstein
gravity. The two classes on which we focus are Kaluza-Klein black holes, i.e.
static solutions with an event horizon in asymptotically flat spaces with
compact directions, and stationary solutions with an event horizon in
asymptotically flat space. Highlights include the recently constructed
multi-black hole configurations on the cylinder and thin rotating black rings
in dimensions higher than five. The phase diagram that is emerging for each of
the two classes will be discussed, including an intriguing connection that
relates the phase structure of Kaluza-Klein black holes with that of
asymptotically flat rotating black holes.Comment: latex, 49 pages, 5 figures. Lectures to appear in the proceedings of
the Fourth Aegean Summer School, Mytiline, Lesvos, Greece, September 17-22,
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