اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThree-point functions in the SU(2) sector at strong coupling
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 $mathcal{N}=4$ 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 $AdS_3 times S^3$ 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.
قيم البحث
اقرأ أيضاً
We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classic
al limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.
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-cha
in 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.
In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the $mathcal{N}=4$ super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis. The struc
ture threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix. We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model. Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified. To determine the analyticity, we develop a new universal logic applicable at both weak and strong couplings. As a result, compact semi-classical formulas are obtained for a general class of three-point functions at weak coupling including the ones whose semi-classical behaviors were not known before. In addition, the new analyticity argument applied to the strong coupling analysis leads to a modification of the integration contour, producing the results consistent with the recent hexagon bootstrap approach. This modification also makes the Frolov-Tseytlin limit perfectly agree with the weak coupling form.
Starting from the known expression for the three-point correlation functions for Liouville exponentials with generic real coefficients at we can prove the Liouville equation of motion at the level of three-point functions. Based on the analytical str
ucture of the correlation functions we discuss a possible mass shell condition for excitations of noncritical strings and make some observations concerning correlators of Liouville fields.
The recently developed gauge-invariant formalism for the treatment of fluctuations in holographic renormalization group (RG) flows overcomes most of the previously encountered technical difficulties. I summarize the formalism and present its applicat
ion to the GPPZ flow, where scattering amplitudes between glueball states have been calculated and a set of selection rules been found.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
