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Register a new userNonrelativistic near-BPS corners of $mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
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We consider limits of $mathcal{N}=4$ super Yang-Mills (SYM) theory that approach BPS bounds and for which an $SU(1,1)$ structure is preserved. The resulting near-BPS theories become non-relativistic, with a $U(1)$ symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $mathcal{N}=4$ SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the $SU(1,1|1)$ near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a $SU(2,1)$ structure is preserved.
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We consider limits of $mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $mathcal{N}=4$ SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with $mathrm{SU}(1,2|2)$ symmetry, which has several new features compared to the previously considered cases with $mathrm{SU}(1,1)$ symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the $mathrm{SU}(1,2|2)$ algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The $mathrm{SU}(1,1|1)$ near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.
We study singular time-dependent $frac{1}{8}$-BPS configurations in the abelian sector of ${{mathcal N}= 4}$ supersymmetric Yang-Mills theory that represent BPS string-like defects in ${{mathbb R}times S^3}$ spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $frac{1}{8}$-BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global $AdS_5times S^5$ that share supersymmetries with a class of dual-giant gravitons. For simple configurations, we demonstrate how to define a good variational problem and propose a regularization scheme that leads to finite energy and global charges on both sides of the holographic correspondence.
We consider the ambitwistor description of $mathcal N$=4 supersymmetric extension of U($N$) Yang-Mills theory on Minkowski space $mathbb R^{3,1}$. It is shown that solutions of super-Yang-Mills equations are encoded in real-analytic U($N$)-valued functions on a domain in superambitwistor space ${mathcal L}_{mathbb R}^{5|6}$ of real dimension $(5|6)$. This leads to a procedure for generating solutions of super-Yang-Mills equations on $mathbb R^{3,1}$ via solving a Riemann-Hilbert-type factorization problem on two-spheres in $mathcal L_{mathbb R}^{5|6}$.
We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $mathcal N = 4$ Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large $N$ supergravity predictions and the numerical finite $N$ results already at $Nsim 100$. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite $N$, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.
We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in $mathcal{N}=4$ SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators $mathcal{O}_J$ of weight $J=2,3,4$. Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.
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