1,802 research outputs found
World-Sheets from N=4 Super Yang-Mills
We examine whether the free energy of N=4 super Yang-Mills theory (SYM) in
four dimensions corresponds to the partition function of the AdS_5 x S^5
superstring when corresponding operators are inserted into both theories. We
obtain a formal free energy of N=4 U(N) SYM in four dimensions generated by the
Feynman graph expansion to all orders of the 't Hooft coupling expansion with
arbitrary N. This free energy is written as the sum over discretized closed
two-dimensional surfaces that are identified with the world-sheets of the
string. We compare this free energy with a formal partition function of the
discretized AdS_5 x S^5 superstring with the kappa-symmetry fixed in the
killing gauge and in the expansion corresponding to the weak 't Hooft coupling
expansion in the SYM. We find common properties on both sides, although further
studies are required to obtain a more precise comparison. Our result suggests a
mechanism for how the world-sheet appears dynamically from N=4 SYM, thus
enabling us to derive how the AdS_5 x S^5 superstring is reproduced in the
AdS/CFT correspondence.Comment: 24 pages, 7 figures, typos corrected, references adde
Zariski Quantization as Second Quantization
The Zariski quantization is one of the strong candidates for a quantization
of the Nambu-Poisson bracket. In this paper, we apply the Zariski quantization
for first quantized field theories, such as superstring and supermembrane
theories, and clarify physical meaning of the Zariski quantization. The first
quantized field theories need not to possess the Nambu-Poisson structure.
First, we construct a natural metric for the spaces on which Zariski product
acts in order to apply the Zariski quantization for field theories. This metric
is invariant under a gauge transformation generated by the Zariski quantized
Nambu-Poisson bracket. Second, we perform the Zariski quantization of
superstring and supermembrane theories as examples. We find flat directions,
which indicate that the Zariski quantized theories describe many-body systems.
We also find that pair creations and annihilations occur among the many bodies
introduced by the Zariski quantization, by studying a simple model. These facts
imply that the Zariski quantization is a second quantization. Moreover, the
Zariski quantization preserves supersymmetries of the first quantized field
theories. Thus, we can obtain second quantized theories of superstring and
supermembranes by performing the Zariski quantization of the superstring and
supermembrane theories.Comment: 18 pages, 2 figure
Moduli Space in Homological Mirror Symmetry
We prove that the moduli space of the pseudo holomorphic curves in the
A-model on a symplectic torus is homeomorphic to a moduli space of Feynman
diagrams in the configuration space of the morphisms in the B-model on the
corresponding elliptic curve. These moduli spaces determine the
structure of the both models.Comment: 21 pages, 8 figure
On the Structure Constants of Volume Preserving Diffeomorphism Algebra
Regularizing volume preserving diffeomorphism (VPD) is equivalent to a long
standing problem, namely regularizing Nambu-Poisson bracket. In this paper, as
a first step to regularizing VPD, we find general complete independent basis of
VPD algebra. Especially, we find complete independent basis that give simple
structure constants, where three area preserving diffeomorphism (APD) algebras
are manifest. This implies that an algebra that regularizes VPD algebra should
include three u(N) Lie algebras.Comment: 8 page
Covariant Formulation of M-Theory II
We propose a supersymmetric model that defines M-theory. It possesses SO(1,
10) super Poincare symmetry and is constructed based on the Lorentzian
3-algebra associated with U(N) Lie algebra. This model is a supersymmetric
generalization of the model in arXiv:0902.1333. From our model, we derive BFSS
matrix theory and IIB matrix model in the naive large N limit by taking
appropriate BPS vacua.Comment: 9 pages, minor change
Born-Infeld Action from Supergravity
We show that the Born-Infeld action with the Wess-Zumino terms for the
Ramond-Ramond fields, which is the D3-brane effective action, is a solution to
the Hamilton-Jacobi (H-J) equation of type IIB supergravity. Adopting the
radial coordinate as time, we develop the ADM formalism for type IIB
supergravity reduced on and derive the H-J equation, which is the
classical limit of the Wheeler-De Witt equation and whose solutions are
classical on-shell actions. The solution to the H-J equation reproduces the
on-shell actions for the supergravity solution of a stack of D3-branes in a
field and the near-horizon limit of this supergravity solution, which is
conjectured to be dual to noncommutative Yang Mills and reduces to in the commutative limit. Our D3-brane effective action is that of
a probe D3-brane, and the radial time corresponds to the vacuum expectation
value of the Higgs field in the dual Yang Mills. Our findings can be applied to
the study of the holographic renormalization group.Comment: 25 pages, minor changes, published versio
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