690 research outputs found
On RG-flow and the Cosmological Constant
The AdS/CFT correspondence implies that the effective action of certain
strongly coupled large gauge theories satisfy the Hamilton-Jacobi equation
of 5d gravity. Using an analogy with the relativistic point particle, I
construct a low energy effective action that includes the Einstein action and
obeys a Callan-Symanzik-type RG-flow equation. It follows from the flow
equation that under quite general conditions the Einstein equations admit a
flat space-time solution, but other solutions with non-zero cosmological
constant are also allowed. I discuss the geometric interpretation of this
result in the context of warped compactifications.Comment: 11 pages, 1 figure, contribution to the proceedings of Strings '99,
misprint correcte
Loop and surface operators in N=2 gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional N=2 gauge
theory has been uncovered by some of the authors. We consider the role of
extended objects in gauge theory, surface operators and line operators, under
this correspondence. We map such objects to specific operators in Liouville
theory. We employ this connection to compute the expectation value of general
supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge
theories.Comment: 60 pages, 11 figures; v3: further minor corrections, published
versio
Quantum States of String-Inspired Lineal Gravity
We construct quantum states for a (1+1) dimensional gravity-matter model that
is also a gauge theory based on the centrally extended Poincar\'e group.
Explicit formulas are found, which exhibit interesting structures. For example
wave functionals are gauge invariant except for a gauge non-invariant phase
factor that is the Kirillov-Kostant 1-form on the (co-) adjoint orbit of the
group. However no evidence for gravity-matter forces is found.Comment: 23 pages in REVTEX, MIT-CTP-227
On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
We review both the construction of conformal blocks in quantum Liouville
theory and the quantization of Teichm\"uller spaces as developed by Kashaev,
Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert
space acted on by a representation of the mapping class group. According to a
conjecture of H. Verlinde, the two are equivalent. We describe some key steps
in the verification of this conjecture.Comment: Contribution to the proceedings of the 6th International Conference
on CFTs and Integrable Models, Chernogolovka, Russia, September 2002; v2:
Typos corrected, typographical change
Automorphisms of the affine SU(3) fusion rules
We classify the automorphisms of the (chiral) level-k affine SU(3) fusion
rules, for any value of k, by looking for all permutations that commute with
the modular matrices S and T. This can be done by using the arithmetic of the
cyclotomic extensions where the problem is naturally posed. When k is divisible
by 3, the automorphism group (Z_2) is generated by the charge conjugation C. If
k is not divisible by 3, the automorphism group (Z_2 x Z_2) is generated by C
and the Altsch\"uler--Lacki--Zaugg automorphism. Although the combinatorial
analysis can become more involved, the techniques used here for SU(3) can be
applied to other algebras.Comment: 21 pages, plain TeX, DIAS-STP-92-4
String loop corrections to the universal hypermultiplet
We study loop corrections to the universal dilaton supermultiplet for type
IIA strings compactified on Calabi-Yau threefolds. We show that the
corresponding quaternionic kinetic terms receive non-trivial one-loop
contributions proportional to the Euler number of the Calabi-Yau manifold,
while the higher-loop corrections can be absorbed by field redefinitions. The
corrected metric is no longer Kahler. Our analysis implies in particular that
the Calabi-Yau volume is renormalized by loop effects which are present even in
higher orders, while there are also one-loop corrections to the Bianchi
identities for the NS and RR field strengths.Comment: 30 pages, harvmac, 1 figure. v2: minor typos corrected. Version to
appear in Classical and Quantum Gravit
Wrapped M2/M5 Duality
A microscopic accounting of the entropy of a generic 5D supersymmetric
rotating black hole, arising from wrapped M2-branes in Calabi-Yau compactified
M-theory, is an outstanding unsolved problem. In this paper we consider an
expansion around the zero-entropy, zero-temperature, maximally rotating ground
state for which the angular momentum J_L and graviphoton charge Q are related
by J_L^2=Q^3. At J_L=0 the near horizon geometry is AdS_2 x S^3. As J_L^2 goes
to Q^3 it becomes a singular quotient of AdS_3 x S^2: more precisely, a
quotient of the near horizon geometry of an M5 wrapped on a 4-cycle whose
self-intersection is the 2-cycle associated to the wrapped-M2 black hole. The
singularity of the AdS_3 quotient is identified as the usual one associated to
the zero-temperature limit, suggesting that the (0,4) wrapped-M5 CFT is dual
near maximality to the wrapped-M2 black hole. As evidence for this, the
microscopic (0,4) CFT entropy and the macroscopic rotating black hole entropy
are found to agree to leading order away from maximality.Comment: 10 pages, no figure
Multivalued Fields on the Complex Plane and Conformal Field Theories
In this paper a class of conformal field theories with nonabelian and
discrete group of symmetry is investigated. These theories are realized in
terms of free scalar fields starting from the simple systems and scalar
fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the
conformal blocks can be explicitly solved. Besides of the fact that one obtains
in this way an entire class of theories in which the operators obey a
nonstandard statistics, these systems are interesting in exploring the
connection between statistics and curved space-times, at least in the two
dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires
harvmac.tex), LMU-TPW 92-1
Free Fields for Chiral 2D Dilaton Gravity
We give an explicit canonical transformation which transforms a generic
chiral 2D dilaton gravity model into a free field theory.Comment: LaTeX file, 4 pages, to appear in Phys. Rev.
Predictions for PP-wave string amplitudes from perturbative SYM
The role of general two-impurity multi-trace operators in the BMN
correspondence is explored. Surprisingly, the anomalous dimensions of all
two-impurity multi-trace BMN operators to order g_2^2\lambda' are completely
determined in terms of single-trace anomalous dimensions. This is due to
suppression of connected field theory diagrams in the BMN limit and this fact
has important implications for some string theory processes on the PP-wave
background. We also make gauge theory predictions for the matrix elements of
the light-cone string field theory Hamiltonian in the two string-two string and
one string-three string sectors.Comment: 46 pages, 12 figures. V3:typos correcte
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