Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Algebraic Curve of Classical Superstrings on AdS_5xS^5
85
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop N=4 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.
rate research
Read More
We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both bosonic and fermionic fields.
We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions.
The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.
Motivated by the notorious difficulties in determining the first quantum corrections to the spectrum of short strings in AdS_5xS^5 from first principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the world-sheet Hamiltonian density is constant along the extension of the string and directly proportional to the square of the spacetime energy. We quantize this system in a minisuperspace approach, in which we consider only a single AdS_5 string mode excitation next to an arbitrary particle like zero-mode contribution in the full AdS_5xS^5 background. We determine the quantum spectrum using this method to the next-to-next-to-leading order in the large t Hooft coupling expansion. We argue for an ordering prescription which should arise from supersymmetrization and indeed recover the integrability based predictions for the spectrum of the lightest excitation, dual to the Konishi field scaling dimensions. The higher excitations fail to agree, but this is shown to be a consequence of the string mode truncation employed. Despite this simple setup, our system reveals intriguing features, such as a close connection to particles in AdS_6, classical integrability and preservation of the isometries of AdS_5xS^5 at the quantum level.
We consider classical superstrings propagating on AdS_5 x S^5 space-time. We consistently truncate the superstring equations of motion to the so-called su(1|1) sector. By fixing the uniform gauge we show that physical excitations in this sector are described by two complex fermionic degrees of freedom and we obtain the corresponding Lagrangian. Remarkably, this Lagrangian can be cast in a two-dimensional Lorentz-invariant form. The kinetic part of the Lagrangian induces a non-trivial Poisson structure while the Hamiltonian is just the one of the massive Dirac fermion. We find a change of variables which brings the Poisson structure to the canonical form but makes the Hamiltonian nontrivial. The Hamiltonian is derived as an exact function of two parameters: the total S^5 angular momentum J and string tension lambda; it is a polynomial in 1/J and in sqrt{lambda} where lambda=frac{lambda}{J^2} is the effective BMN coupling. We identify the string states dual to the gauge theory operators from the closed su(1|1) sector of N=4 SYM and show that the corresponding near-plane wave energy shift computed from our Hamiltonian perfectly agrees with that recently found in the literature. Finally we show that the Hamiltonian is integrable by explicitly constructing the corresponding Lax representation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
