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

Mirror Adaptation in Sensory-Motor Simultaneity

Background: When one watches a sports game, one may feel her/his own muscles moving in synchrony with the player's. Such parallels between observed actions of others and one's own has been well supported in the latest progress in neuroscience, and coined “mirror system.” It is likely that due to such phenomena, we are able to learn motor skills just by observing an expert's performance. Yet it is unknown whether such indirect learning occurs only at higher cognitive levels, or also at basic sensorimotor levels where sensorimotor delay is compensated and the timing of sensory feedback is constantly calibrated. Methodology/Principal Findings: Here, we show that the subject's passive observation of an actor manipulating a computer mouse with delayed auditory feedback led to shifts in subjective simultaneity of self mouse manipulation and auditory stimulus in the observing subjects. Likewise, self adaptation to the delayed feedback modulated the simultaneity judgment of the other subjects manipulating a mouse and an auditory stimulus. Meanwhile, subjective simultaneity of a simple visual disc and the auditory stimulus (flash test) was not affected by observation of an actor nor self-adaptation. Conclusions/Significance: The lack of shift in the flash test for both conditions indicates that the recalibration transfer is specific to the action domain, and is not due to a general sensory adaptation. This points to the involvement of a system for the temporal monitoring of actions, one that processes both one's own actions and those of others

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

A counterexample to the CFT convexity conjecture

Motivated by the weak gravity conjecture, arXiv:2108.04594 conjectured that in any CFT, the minimal operator dimension at fixed charge is a convex function of the charge. In this letter we construct a counterexample to this convexity conjecture, which is a clockwork-like model with some modifications to make it a weakly-coupled CFT. We also discuss further possible applications of this model and some modified versions of the conjecture which are not ruled out by the counterexample

Single and multiple Gunn diode oscillator using an image NRD guide

A single and a multiple Gunn diode oscillator using an image NRD guide have been investigated. The LSM01 mode which is the operating mode of the image NRD guide can be the dominant mode because undesired modes are suppressed due to existence of the image plane. In experiments at X-band for oscillators with Gunn diodes mounted in the dielectric strip of the image NRD guide, the oscillation frequencies could be varied by a movable shorting plane for the single diode case and an effective power combining operation was obtained for the double diode cas