Resurgence in Deformed Integrable Models

Resurgence has been shown to be a powerful and even necessary technique to understand many physical system. The study of perturbative methods in general quantum field theories is hard, but progress is often possible in reduced settings, such as integrable models. In this thesis, we study resurgent effects in integrable deformations of two-dimensional σ-models in two settings.First, we study the integrable bi-Yang-Baxter deformation of the SU(2) principal chiral model (PCM) and find finite action uniton and complex uniton solutions. Under an adiabatic compactification on an S1, we obtain a quantum mechanical system with an elliptic Lam´e-like potential. We perform a perturbative calculation of the ground state energy of this quantum mechanical system to large orders obtaining an asymptotic series. Using the Borel-Pad´e technique, we determine that the locations of branch cuts in the Borel plane match the values of the uniton and complex uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutionswhich fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an N = 2 Seiberg-Witten theory. This can be done either as an Nf = 4 SU(2) theory or as an elliptic SU(2) × SU(2) quiver theory. The mass parameters of the gauge theory are given in terms of the bi-Yang-Baxter deformation parameters.Second, we perform a perturbative expansion of the thermodynamic Bethe ansatz (TBA) equations of the SU(N) λ-model with WZW level k in the presence of a chemical potential. This is done with its exact S-matrix and the recently developed techniques [1, 2] using a Wiener-Hopf decomposition, which involve a careful matching of bulk and edge ans¨atze. We determine the asymptotic expansion of this series and compute its renormalon ambiguities in the Borel plane. The analysis is supplemented by a parallel solution of the TBA equations that results in a transseries. The transseries comes with an ambiguity that is shown to precisely match the Borel ambiguity. It is shown that the leading IR renormalon vanishes when k is a divisor of N

Resurgence in the bi-Yang-Baxter model

We study the integrable bi-Yang-Baxter deformation of the SU(2) principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an S1 , we obtain a quantum mechanics with an elliptic Lamé-like potential.We perform a perturbative calculation of the ground state energy in this quantum mechanics to large orders obtaining an asymptotic series. Using the Borel-Padé technique, we determine the expected locations of branch cuts in the Borel plane of the perturbative series and show that they match the values of the uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutions which fractionate upon adiabatic compactification.An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an N=2 Seiberg-Witten theory. This can be done either as an Nf=4 SU(2) theory or as an elliptic quiver SU(2) x SU(2) theory. The mass parameters of the gauge theory are given by the deformation parameters of the PCM

Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d

We enlarge the dictionary between matrix models for long linear quivers preserving eight supercharges in $d=5$ and $d=3$ and type IIB supergravity backgrounds with AdS$_{d+1}$ factors. We introduce mass deformations of the field theory that break the quiver into a collection of interacting linear quivers, which are decoupled at the end of the RG flow. We find and solve a Laplace problem in supergravity which realises these deformations holographically. The free energy and expectation values of antisymmetric Wilson loops are calculated on both sides of the proposed duality, finding agreement. Our matching procedure sheds light on the F-theorem in five dimensions.Comment: 46 pages plus appendices. Various figures. Some improvements and references added. SciPost Physics versio

Percutaneous reduction and fixation of intraarticular calcaneal fractures

Objective: Percutaneous reduction by distraction and subsequent percutaneous screw fixation to restore calcaneal and posterior talocalcaneal facet anatomy. The aim of this technique is to improve functional outcome and to diminish the rate of secondary posttraumatic arthrosis compared to conservative treatment and, secondly, to reduce infectious complications compared to open reduction and internal fixation (ORIF). Indications: Sanders type II-IV displaced intraarticular calcaneal fractures. Contraindications: Isolated centrally depressed fragment. Contraindications: Patients who are expected to be noncompliant. Surgical Technique: Four distractors (Synthes™) are positioned, two on each side of the foot, between the tuberosity of the calcaneus and talus and between the tuberosity and cuboid. A distracting force is given over all four distractors. A blunt drifter is then introduced from the plantar side to unlock and push up any remaining depressed parts of the subtalar joint surface of the calcaneus. The reduction is fixated with two or three screws inserted percutaneously. Postoperative Management: Directly postoperatively, full active range of motion exercises of the ankle joint can start, with the foot elevated in the 1st postoperative week. Stitches are removed after 14 days. Implant removal is necessary in 50-60% of patients. Results: Between 1999 and 2004, 59 patients with 71 fractures were treated by percutaneous skeletal triangular distraction and percutaneous fixation. A total of 50 patients with 61 fractures and a minimum follow-up of 1 year were available for follow-up. According to the American Orthopaedic Foot and Ankle Society Hindfoot Score, 72% had a good to excellent result. A secondary subtalar arthrodesis was performed in five patients and planned in four (total 15%). Böhler's angle increased by about 20° postoperatively. Sagittal motion was 90% andsubtalar motion 70% compared to the healthy foot

Total synthesis of decarboxyaltenusin

The total synthesis of decarboxyaltenusin (5’-methoxy-6-methyl-[1,1’-biphenyl]-3,3’,4-triol), a toxin produced by various mold fungi, has been achieved in seven steps in a yield of 31% starting from 4-methylcatechol and 1-bromo-3,5-dimethoxybenzene, where the longest linear sequence consists of five steps. The key reaction was a palladium-catalyzed Suzuki coupling of an aromatic boronate with a brominated resorcin derivative

Extended Lateral Approach for Intra-articular Calcaneal Fractures: An Inverse Relationship between Surgeon Experience and Wound Complications

The current reference standard for the treatment of displaced intra-articular calcaneal fractures is open reduction and internal fixation using an extended lateral approach. In the present retrospective study, we evaluated the results of a consecutive series of patients treated in the same fashion from June 2005 to September 2011 using a subcuticular single-layer closure technique. We also determined the risk factors for the development of wound complications and the rate of wound complications. Also, we assessed which patient, fracture, and surgical characteristics affected these complications. During the 75-month study period, we operated on 53 displaced intra-articular calcaneal fractures in 50 patients using the extended lateral approach. The incision was closed using the subcuticular technique in 49 cases (92.45%). In the subcuticular closure group 2 (4.1%) deep infections and 2 (4.1%) superficial wound complications (1 dehiscence and 1 infection) occurred. Wound edge or flap necrosis was not encountered. The use of bone-void filler and the experience of the surgical team were significantly (p < .001 and p = .026, respectively) associated with the occurrence of wound complications. The subcuticular single-layer suture technique is a suitable closure technique in the treatment of displaced intra-articular calcaneal fractures. It was associated with a low complication rate combined with the extended lateral approach. The effect of bone void fillers on the incidence of complications should receive more attention in future research. The association between wound complications and the experience level of the surgical team supports the need for centralization of this complex injury

Percutaneous treatment of displaced intra-articular calcaneal fractures

Background. The outcome after displaced intra-articular calcaneal fractures is influenced by the condition of the surrounding soft tissues. To avoid secondary soft tissue complications after surgical treatment, several less-invasive procedures for reduction and fixation have been introduced. The percutaneous technique according to Forgon and Zadravecz is suitable for all types of displaced intra-articular calcaneal fractures and was therefore introduced in our clinic. The aim of this study was to evaluate the lon

Closing the medullary canal after retrograde nail removal using a bioabsorbable bone plug: technical tip

We describe a simple technique for closure of the intra-articular opening after the removal of a retrograde femur nail. With the use of a gelatine bioabsorbable bone plug the medullary canal is closed, reducing leakage of blood and cancellous bone particles from the bone into the knee joint

Subtalar versus triple arthrodesis after intra-articular calcaneal fractures

Depending upon initial treatment, between 2 and 30% of patients with a displaced intra-articular calcaneal fracture require a secondary arthrodesis. The aim of this study was to investigate the effect of subtalar versus triple arthrodesis on functional outcome. A total of 33 patients with 37 secondary arthrodeses (17 subtalar and 20 triple) with a median follow-up of 116 months were asked to complete questionnaires regarding disease-specific functional outcome (Maryland Foot Score, MFS), quality of life (SF-36) and overall satisfaction with the treatment (Visual Analogue Scale, VAS). Patient groups were comparable considering median age at fracture, initial treatment (conservative or operative), time to arthrodesis, median follow-up, and post-arthrodesis radiographic angles. The MFS score was similar after subtalar versus triple arthrodesis (59 vs. 56 points; P = 0.79). No statistically significant difference was found for the SF-36 (84 vs. 83 points; P = 0.67) and the VAS (5 vs. 6; P = 0.21). Smoking was statistically significantly associated with a non-union (χ2 = 6.60, P = 0.017). The current study suggests that there is no significant difference in functional outcome between an in situ subtalar or triple arthrodesis as a salvage technique for symptomatic arthrosis after an intra-articular calcaneal fracture. Smoking is a risk factor for non-union

Hemi-Castaing ligamentoplasty for the treatment of chronic lateral ankle instability: a retrospective assessment of outcome

Purpose: In the treatment of chronic ankle instability, most non-anatomical reconstructions use the peroneus brevis tendon. This, however, sacrifices the natural ankle stabilising properties of the peroneus brevis muscle. The aim of this study was to evaluate the functional outcome of patients treated with a hemi-Castaing procedure, which uses only half the peroneus brevis tendon. Methods: We performed a retrospective cohort study of patients who underwent hemi-Castaing ligamentoplasty for chronic lateral ankle instability between 1993 and 2010, with a minimum of one year follow-up. Patients were sent a postal questionnaire comprising five validated outcome measures: Olerud-Molander Ankle Score (OMAS), Karlsson Ankle Functional Score (KAFS), Tegner Activity Level Score (pre-injury, prior to surgery, at follow-up), visual analog scale on pain (VAS) and the Short Form 36 (SF-36). Results: Twenty patients completed the questionnaire on functional outcome. The OMAS showed good to excellent outcome in 80% and the KAFS in 65%, the Tegner Score improved from surgery but did not reach pre-injury levels, the VAS on pain was 1 of 10 and the SF-36 returned to normal compared with the average population. Conclusions: Even though most patients were satisfied with the results, outcome at long-term follow-up was less favourable compared with the literature on anatomical reconstructions. In accordance with the literature, we therefore conclude that the initial surgical treatment of chronic lateral ankle instability should be an anatomical repair with augmentation (i.e. the Broström-Gould technique) and the non-anatomical repair should be reserved for unsuccessful cases after anatomical repair or in cases where no adequate ligament remnants are available for reconstruction