112 research outputs found
Operator Formulation of Green-Schwarz Superstring in the Semi-Light-Cone Conformal Gauge
In this article we present a comprehensive account of the operator
formulation of the Green-Schwarz superstring in the semi-light-cone (SLC)
gauge, where the worldsheet conformal invariance is preserved. Starting from
the basic action, we systematically study the symmetry structure of the theory
in the SLC gauge both in the Lagrangian and the phase space formulations. After
quantizing the theory in the latter formulation we construct the quantum
Virasoro and the super-Poincare generators and clarify the closure properties
of these symmetry algebras. Then by making full use of this knowledge we will
be able to construct the BRST-invariant vertex operators which describe the
emission and the absorption of the massless quanta and show that they form the
appropriate representation of the quantum symmetry algebras. Furthermore, we
will construct an exact quantum similarity transformation which connects the
SLC gauge and the familiar light-cone (LC) gauge. As an application
BRST-invariant DDF operators in the SLC gauge are obtained starting from the
corresponding physical oscillators in the LC gauge.Comment: 88 pages, ptptex, no figure. Some clarifications are made and a
reference is added in section 6. Published versio
Three-point functions in the SU(2) sector at strong coupling
Extending the methods developed in our previous works (arXiv:1110.3949,
arXiv:1205.6060), we compute the three-point functions at strong coupling of
the non-BPS states with large quantum numbers corresponding to the composite
operators belonging to the so-called SU(2) sector in the
super-Yang-Mills theory in four dimensions. This is achieved by the
semi-classical evaluation of the three-point functions in the dual string
theory in the spacetime, using the general one-cut finite
gap solutions as the external states. In spite of the complexity of the
contributions from various parts in the intermediate stages, the final answer
for the three-point function takes a remarkably simple form, exhibiting the
structure reminiscent of the one obtained at weak coupling. In particular, in
the Frolov-Tseytlin limit the result is expressed in terms of markedly similar
integrals, however with different contours of integration. We discuss a natural
mechanism for introducing additional singularities on the worldsheet without
affecting the infinite number of conserved charges, which can modify the
contours of integration.Comment: 128 pages (A summary is given in section 1); v2 minor improvement
On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
As a step toward uncovering the relation between the weak and the strong
coupling regimes of the super Yang-Mills theory beyond the
specral level, we have developed in a previous paper [arXiv:1410.8533] a novel
group theoretic interpretation of the Wick contraction of the fields, which
allowed us to compute a much more general class of three-point functions in the
SU(2) sector, as in the case of strong coupling [arXiv:1312.3727], directly in
terms of the determinant representation of the partial domain wall partition
funciton. Furthermore, we derived a non-trivial identity for the three point
functions with monodromy operators inserted, being the discrete counterpart of
the global monodromy condition which played such a crucial role in the
computation at strong coupling. In this companion paper, we shall extend our
study to the entire sector and obtain several important
generalizations. They include in particular (i) the manifestly conformally
covariant construction, from the basic principle, of the singlet-projection
operator for performing the Wick contraction and (ii) the derivation of the
monodromy relation for the case of the so-called "harmonic R-matrix", as well
as for the usual fundamental R-matrtix. The former case, which is new and has
features rather different from the latter, is expected to have important
applications. We also describe how the form of the monodromy relation is
modified as is reduced to its subsectors.Comment: 49+10 pages;v3 Published version. Typos corrected. Explicit form of
the monodromy relations for the three-point functions displaye
Novel construction and the monodromy relation for three-point functions at weak coupling
In this article, we shall develop and formulate two novel viewpoints and
properties concerning the three-point functions at weak coupling in the SU(2)
sector of the N = 4 super Yang-Mills theory. One is a double spin-chain
formulation of the spin-chain and the associated new interpretation of the
operation of Wick contraction. It will be regarded as a skew symmetric pairing
which acts as a projection onto a singlet in the entire SO(4) sector, instead
of an inner product in the spin-chain Hilbert space. This formalism allows us
to study a class of three-point functions of operators built upon more general
spin-chain vacua than the special configuration discussed so far in the
literature. Furthermore, this new viewpoint has the signicant advantage over
the conventional method: In the usual "tailoring" operation, the Wick
contraction produces inner products between off-shell Bethe states, which
cannot be in general converted into simple expressions. In contrast, our
procedure directly produces the so-called partial domain wall partition
functions, which can be expressed as determinants. Using this property, we
derive simple determinantal representation for a broader class of three-point
functions. The second new property uncovered in this work is the non-trivial
identity satisfied by the three-point functions with monodromy operators
inserted. Generically this relation connects three-point functions of different
operators and can be regarded as a kind of Schwinger-Dyson equation. In
particular, this identity reduces in the semiclassical limit to the triviality
of the product of local monodromies around the vertex operators, which played a
crucial role in providing all important global information on the three-point
function in the strong coupling regime. This structure may provide a key to the
understanding of the notion of "integrability" beyond the spectral level.Comment: 35 pages;v2 Minor corrections made. An appendix and references
added;v3 Typos correcte
On the conservation of electric charge around a monopole of finite size
In monopole-fermion dynamics, the boundary condition which is responsible for baryon number non-conservation also violates electric and color hypercharge conservation. We show by detailed calculations that actually the latter conservation laws are dynamically restored. It is shown that for a finite size monopole, there is a small but finite amplitude for the monopole ground state to make a virtual transition into a state containing a dyon and some fermions carrying equal and opposite charge as that of the dyon. But the amplitude for this state to make a virtual transition to a state carrying a net total charge is identically zero. The monopole ground state, as a result, is an eigenstate of electric charge even in the presence of massless fermions. We also calculate the four-body charge and chirality conserving but baryon number violating condensates, which exist independently of the existence of the anomaly and hence persist even in the presence of more generations of massless fermions
- …