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 $\mathcal{N}=4$ 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 ${\rm psu}(2,2|4)$ 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 ${\rm psu}(2,2|4)$ 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

Slow Slip Events in the Kanto and Tokai Regions of Central Japan Detected Using Global Navigation Satellite System Data During 1994–2020

Slow slip events (SSEs) along subduction zones play an important role in accommodating relative plate motion. SSEs interplay with large megathrust earthquakes and other slow earthquakes, including low frequency and very low frequency earthquakes. The Kanto and Tokai regions of central Japan host frequent slow and large earthquakes, with significant differences in slip behavior along the subduction zones in the Suruga Trough, Sagami Trough, and Japan Trench. In this study, we conducted a systematic search to estimate the fault models and durations of short-term SSEs using continuous Global Navigation Satellite System data collected from 1994 to 2020. We detected 176 potential SSEs with moment magnitudes of 5.3–7.0 and durations of 0–80 days from the time series. Along the Sagami Trough, two shallow regions at a depth of 10–20 km host Mw ≥ 6.5 SSEs off of the Boso Peninsula and accommodate most of the relative plate motion aseismically. Some SSEs also occur on the deep plate interface down to ∼50 km without tectonic tremors. Along the Japan Trench, the cumulative slip of the SSEs exhibits a bi-modal depth distribution to avoid the large slip areas of past megathrust earthquakes at 30–40 km depth. The shallow SSEs are in the same depth range (10–30 km) as tectonic tremors, but are spatially separate from tremors along the trench. The detected SSEs have limited temporal correlations with other slow earthquakes and earthquake swarms, which suggests that many factors control the genesis of slow and regular earthquakes

Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.Comment: 31 pages + appendices; v2 References adde

Characteristics of postseismic deformation following the 2003 Tokachi-oki earthquake and estimation of the viscoelastic structure in Hokkaido, northern Japan

Additional file 1. This file includes additional figures ‘Figures S1–S9’ and their captions

Development of an Epidemic‐type Aftershock‐sequence Model Explicitly Incorporating the Seismicity‐triggering Effects of Slow Slip Events

Slow slip events (SSEs) at subduction zone plate boundaries sometimes trigger earthquake swarms and megathrust earthquakes. The causal relationship between SSEs and seismicity has been studied worldwide, but the epidemic-type aftershock-sequence (ETAS) model, which is a standard statistical model of seismicity, does not explicitly consider the seismicity-triggering effect of SSEs. Therefore, if an SSE occurs at a plate boundary, probabilistic earthquake forecasts based on the ETAS model fail to predict observed seismicity. Here, we constructed a statistical model named the SSE-modulated ETAS model by incorporating SSE moment rates estimated from observation data from the global navigation satellite system into the original ETAS model. Our model assumes a linear or power-law relationship between the SSE moment rates and seismicity rates and estimates its proportionality constant as a new ETAS parameter. We applied this new model to three SSEs and M 2.5 or greater earthquakes in the shallow part of the Hikurangi Trench, New Zealand. The results show that it is better than the original ETAS model, giving a significant reduction in the Akaike information criterion. In addition, we examined the functional forms (e.g., lag time and power exponent) of the equation relating the moment rate of the SSEs to the seismicity rate. We also examine the influence of SSEs on aftershock productivity. Our model can improve short-term forecasts of seismicity associated with SSEs if the detection and characterization of SSEs can be done in near real time. Our model is also useful for quantifying characteristics of SSE-induced seismicity

Systematic Detection of Short‐Term Slow Slip Events in Southcentral Alaska

Slow slip events (SSEs) are important for the slip budget along a megathrust fault. Although the recurrence of weeks-long short-term SSEs (S-SSEs) in southcentral Alaska has been suggested, a large amount of noise prevented us from detecting discrete events. We applied a systematic detection method to Global Navigation Satellite System data and detected 31 S-SSEs during the 14-year analysis period. The events mainly occurred at a depth from 35 to 45 km at a down-dip extension of the 1964 Alaska earthquake, and the active clusters correlated with the region of the subducting Yakutat microplate. A large cumulative slip of S-SSEs indicated a significant contribution to stress transfer along the plate interface, and its source area spatially coincided with that of the long-term SSEs and the afterslip of the 1964 earthquake. Large and recurrent S-SSEs are key phenomena for understanding interplate slip kinematics in this region

Episodic transient deformation revealed by the analysis of multiple GNSS networks in the Noto Peninsula, central Japan

流体とスロースリップに駆動された能登半島群発地震 --ソフトバンク独自基準点データを用いた地殻変動解析結果--. 京都大学プレスリリース. 2023-06-13.Since November 30, 2020, an intense seismic swarm and transient deformation have been continuously observed in the Noto Peninsula, central Japan, which is a non-volcanic/geothermal area far from major plate boundaries. We modeled transient deformation based on a combined analysis of multiple Global Navigation Satellite System (GNSS) observation networks, including one operated by a private sector company (SoftBank Corp.), relocated earthquake hypocenters, and tectonic settings. Our analysis showed a total displacement pattern over 2 years shows horizontal inflation and uplift of up to ~ 70 mm around the source of the earthquake swarm. In the first 3 months, the opening of the shallow-dipping tensile crack had an estimated volumetric increase of ~ 1.4 × 10⁷ m³ at a depth of ~ 16 km. Over the next 15 months, the observed deformation was well reproduced by shear-tensile sources, which represent an aseismic reverse-type slip and the opening of a southeast-dipping fault zone at a depth of 14–16 km. We suggest that the upwelling fluid spread at a depth of ~ 16 km through an existing shallow-dipping permeable fault zone and then diffused into the fault zone, triggering a long-lasting sub-meter aseismic slip below the seismogenic depth. The aseismic slip further triggered intense earthquake swarms at the updip