On the Large RR-charge Expansion in N=2{\mathcal N} = 2 Superconformal Field Theories

In this note we study two point functions of Coulomb branch chiral ring elements with large $R$-charge, in quantum field theories with ${\mathcal N} = 2$ superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of arXiv:1706.05743, to estimate the two-point function $${\mathcal Y}_n \equiv |x-y|^{2n\Delta_{\mathcal O}}\left<({\mathcal O}(x))^n(\bar{\mathcal O}(y))^n\right>$$ in the limit where the operator insertion On has large total $R$-charge ${\mathcal J} = n\Delta_{\mathcal O}$. We show that ${\mathcal Y}_n$ has a nontrivial but universal asymptotic expansion at large ${\mathcal J}$, of the form $${\mathcal Y}_n = {\mathcal J}! \left(\frac{\left| {\mathbf N}_{\mathcal O}\right|}{2\pi}\right)^{2{\mathcal J}}{\mathcal J}^\alpha {\tilde{\mathcal Y}}_n$$ where ${\mathcal Y}_n$ approaches a constant as $n\to\infty$, and ${\mathbf N}_{\mathcal O}$ is an $n$-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent $\alpha$ is a positive number proportional to the difference between the $a$-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions against exact results from supersymmetric localization of Baggio et. al. and Gerchkovitz et. al., and find precise agreement for the logarithm ${\mathcal B}_n = \log{\mathcal Y}_n$, up to and including order $\log{\mathcal J}$. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of Argyres et. al. In this way, we show the large-$R$-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua.Comment: minor change

Operator Dimensions from Moduli

We consider the operator spectrum of a three-dimensional ${\cal N} = 2$ superconformal field theory with moduli spaces of one complex dimension, such as the fixed point theory with three chiral superfields $X,Y,Z$ and a superpotential $W = XYZ$. By using the existence of an effective theory on each branch of moduli space, we calculate the anomalous dimensions of certain low-lying operators carrying large $R$-charge $J$. While the lowest primary operator is a BPS scalar primary, the second-lowest scalar primary is in a semi-short representation, with dimension exactly $J+1$, a fact that cannot be seen directly from the $XYZ$ Lagrangian. The third-lowest scalar primary lies in a long multiplet with dimension $J+2 - c_{-3} \, J^{-3} + O(J^{-4})$, where $c_{-3}$ is an unknown positive coefficient. The coefficient $c_{-3}$ is proportional to the leading superconformal interaction term in the effective theory on moduli space. The positivity of $c_{-3}$ does not follow from supersymmetry, but rather from unitarity of moduli scattering and the absence of superluminal signal propagation in the effective dynamics of the complex modulus. We also prove a general lemma, that scalar semi-short representations form a module over the chiral ring in a natural way, by ordinary multiplication of local operators. Combined with the existence of scalar semi-short states at large $J$, this proves the existence of scalar semi-short states at all values of $J$. Thus the combination of ${\cal N}=2$ superconformal symmetry with the large-$J$ expansion is more powerful than the sum of its parts.Comment: 48 pages, 8 figures, LaTeX, typos correcte

Electron spin resonance shifts in S=1 antiferromagnetic chains

We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy based on several effective field theories, the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid, we have to take interactions among magnons into account. Though the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in Haldane phase. We present that our theory gives quantitative agreements with recent ESR experimental results on an spin-1 chain compounds NDMAP

Effective String Theory Simplified

In this set of notes we simplify the formulation of the Poincare'-invariant effective string theory in D dimensions by adding an intrinsic metric and embedding its dynamics into the Polyakov formalism. We use this formalism to construct operators order by order in the inverse physical length of the string, in a fully gauge-invariant framework. We use this construction to discuss universality and nonuniversality of observables up to and including next-to-next-to-leading order in the long string expansion.Comment: v. 3, minor change

A Note on Inhomogeneous Ground States at Large Global Charge

In this note we search for the ground state, in infinite volume, of the $D=3$ Wilson-Fisher conformal $O(4)$ model, at nonzero values of the two independent charge densities $\rho_{1,2}$. Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios $\rho_1 / \rho_2$. This result confirms, within the context of a well-defined effective theory, a recent no-go result of Alvarez-Gaume' et al. We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of $\rho_1 / \rho_2$ containing a neighborhood of zero. This suggests that the scale of variation of the ground state solution in finite volume will be the infrared scale, and that the use of the effective theory at large charge in finite volume is self-consistent.Comment: 13 pages, LaTe

On the Large R-charge Expansion in N=2 Superconformal Field Theories

In this note we study two point functions of Coulomb branch chiral ring elements with large R-charge, in quantum field theories with N = 2 superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of [1], to estimate the two-point correlation function Yn ≡ |x − y|2n∆O(O(x))n(O¯(y))n�in the limit where the operator insertion On has large total R-charge J = n∆O. We show that Yn has a nontrivial but universal asymptotic expansion at large J , of the form Yn = J !�|NO|2π�2JJα Y˜n ,where Y˜ n approaches a constant as n → ∞, and NO is an n-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent α is a positive number proportional to the difference between the a-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions for the logarithm Bn = log(Yn), up to and including order log(J ) against exact results from supersymmetric localization [2–5]. In the case of N = 4 we find precise agreement and in the case N = 2 we find reasonably good numerical agreement at J ' 60 using the no-instanton approximation to the S 4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6–9]. In this way, we show the large-R-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua

The final fate of instability of Reissner-Nordstr\"om-anti-de Sitter black holes by charged complex scalar fields

We investigate instability of 4-dimensional Reissner-Nordstr\"om-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of the hairly black hole is always larger than the one of the unstable RN-AdS$_4$ black hole in the microcanonical ensemble. Our results support the speculation that the black hole with charged scalar hair always appears as the final fate of the instability of the RN-AdS$_4$ black hole.Comment: 9 pages, 4 figures. To appear in PR

On the Large R-charge Expansion in N=2 Superconformal Field Theories

In this note we study two point functions of Coulomb branch chiral ring elements with large R-charge, in quantum field theories with N = 2 superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of [1], to estimate the two-point correlation function Yn ≡ |x − y|2n∆O(O(x))n(O¯(y))n�in the limit where the operator insertion On has large total R-charge J = n∆O. We show that Yn has a nontrivial but universal asymptotic expansion at large J , of the form Yn = J !�|NO|2π�2JJα Y˜n ,where Y˜ n approaches a constant as n → ∞, and NO is an n-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent α is a positive number proportional to the difference between the a-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions for the logarithm Bn = log(Yn), up to and including order log(J ) against exact results from supersymmetric localization [2–5]. In the case of N = 4 we find precise agreement and in the case N = 2 we find reasonably good numerical agreement at J ' 60 using the no-instanton approximation to the S 4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6–9]. In this way, we show the large-R-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua

Prone-Position Thoracoscopic Ligation of the Thoracic Duct for Chyle Leak Following Radical Neck Dissection in a Patient with a Right Aortic Arch

A chyle leak can occur as a complication after neck or chest surgery. Such a leak prolongs the hospital stay and is sometimes life-threatening. The treatment options are conservative management, interventional radiologic embolization, and surgery. Thoracoscopic ligation of the thoracic duct has emerged as a promising and definitive treatment. The case of a 65-year-old Japanese male patient with a rare congenital right aortic arch (typeⅢB1 of Edwardʼs classification) and a severe chyle leak that occurred after a total pharyngolaryngo-esophagectomy (TPLE) is described. The chyle leak was successfully managed by thoracoscopic ligation of the thoracic duct via a left-side approach with the patient in the prone position