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Abstract We study orientifold projections of families of four-dimensional N $$ \mathcal{N} $$ = 1 toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise, in general, to inequivalent models. A suitable orientifold projection relates a subfamily of the latter by conformal duality. That is, there exist exactly marginal deformations that connect the projected models. The deformations take the form of a sign flip in some of the superpotential interactions, similarly to the β-deformation of N $$ \mathcal{N} $$ = 4 SYM. Our construction generalizes previous results on the orientifold projections of the PdP3b and PdP3c singularities.

Abstract We compute the Lens space index for 4d supersymmetric gauge theories involving symplectic gauge groups. This index can distinguish between different gauge groups from a given algebra and it matches across theories related by supersymmetric dualities. We provide explicit calculations for N $$ \mathcal{N} $$ = 4 SYM and for classes of N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 1 Lagrangian quivers related by S-duality. In these cases the index matches across the S-dual phases, while models in different S-duality orbits have a different Lens index. We provide analogous computations for a 4d N $$ \mathcal{N} $$ = 1 toric quiver gauge theory corresponding to a ℤ7 orbifold of ℂ3. This SU(n)7 gauge theory becomes interesting in the case of n = 2 because it is conformally dual to other two models, with symplectic and unitary gauge groups, bifundamentals and antisymmetric tensors. We explicitly check this triality at the level of the Lens space index.

Abstract Background Mesenchymal neoplasms of the uterus encompass a diverse group of tumors, with varying characteristics and origins, collectively accounting for 8% of uterine malignancies. The most common variants include uterine leiomyosarcoma, low‐grade and high‐grade endometrial stromal sarcoma, adenosarcoma, and undifferentiated sarcoma. Clinical presentation is often nonspecific and can lead to delayed diagnosis. Uterine sarcomas are generally aggressive, resulting in poorer prognosis compared to carcinomas. Recent advances in molecular techniques, such as next‐generation sequencing (NGS), have led to the identification of new subtypes of uterine sarcomas, including COL1A1::PDGFB fusion‐associated fibrosarcoma, which has a specific chromosomal translocation t(17;22)(q22;q13). Imatinib, a tyrosine kinase inhibitor (TKI), is an effective treatment for dermatofibrosarcoma protuberans (DFSP), marked by this translocation. Case We present the case of a 42‐year‐old woman diagnosed with COL1A1::PDGFB fusion‐associated uterine fibrosarcoma. The patient underwent total hysterectomy and excision of the tumor, initially misdiagnosed as a low‐grade leiomyosarcoma. Subsequent histological examination, immunohistochemistry, and fluorescence in situ hybridization (FISH) confirmed the diagnosis. After 10 months, disease recurrence was detected, and Imatinib therapy was initiated at a dose of 400 mg daily. An allergic reaction led to a temporary discontinuation, but upon resumption with appropriate medication, a positive radiological response was observed. The patient achieved a complete remission after 2 years and is still on Imatinib treatment. Conclusions COL1A1::PDGFB fusion‐associated uterine fibrosarcoma is an extremely rare mesenchymal neoplasm. In a case we present herein, we treated a patient with imatinib as first‐line medical therapy. The patient is currently in complete remission after 37 months from treatment start. To the best of our knowledge, this represents a unique observation. We also provide a detailed literature review of the published cases so far. Prospective case series are needed to further understand the natural history of these tumors and optimize treatment strategies.

Abstract Background NUT carcinoma (NUTc) is a rare and aggressive malignant epithelial tumor characterized by rearrangement of the NUT gene on chromosome 15q14. Methods In this article, we present the fifth case worldwide of a young woman affected by a NUTc arising from a submandibular gland, presenting as a rapidly evolving mass. She underwent a right scialoadenectomy and received the initial diagnosis of high‐grade mucoepidermoid carcinoma. Due to evidence of local recurrence at magnetic resonance imaging 1 month later, a subsequent right radical neck dissection was performed. The patient then sought a second opinion at our cancer center and finally received the correct diagnosis of NUT carcinoma. Given the well‐known aggressive behavior of this neoplasm, as well as clinical and radiological features, she underwent adjuvant chemo‐radiation (intensity‐modulated radiotherapy + concurrent chemotherapy with cisplatin). Results After a disease‐free interval of 2.6 months, a widespread metastatic disease led to rapid deterioration of performance status and patient death in a few weeks after metastatic onset. Conclusions We presented a case of NUTc arising from salivary gland aiming to improve the knowledge of this rare malignancy. First, we pointed out that in the setting of rare tumors like salivary gland cancers, the diagnosis should be obtained by expert pathologists, and patients should be referred to tertiary cancer centers for their clinical management. Second, molecular profiling may help to identify possible druggable targets that may be exploited to treat patients suffering from this aggressive malignancy. Sharing the molecular data provided in this case will be useful for further research.

Abstract We study 3d 𝒩 = 2 dualities arising from the compactification of 4d 𝒩 = 1 Usp(2n) SQCD with two antisymmetric rank-two tensors and D k+2-type superpotential, with odd k. The analysis is carried out by using field theory methods and by checking the various steps on the three sphere partition function. Most of the results are based on a conjectural confining duality that we do not prove but that fits consistently with the web of dualities that we obtain. Along the analysis we recover dualities already claimed in the literature and we propose new ones. The final picture that emerges fits with the general scheme worked out for ordinary SQCD and for adjoint SQCD with A k -type superpotentials.

Abstract We study various orientifold projections of 4d N $$ \mathcal{N} $$ = 1 toric gauge theories, associated with CY singularities known as L a,b,a /ℤ2, with a + b even. We obtain superconformal chiral theories that have the same central charge, anomalies and superconformal index, whereas they were different before the orientifold. Some of these projections are implemented by a novel type of orientifold without fixed loci, known as glide orientifold. We claim that these theories flow to the same conformal manifold, and they are connected by quadratic exactly marginal deformations. The latter can be written in terms of conjugate pairs of bifundamental fields of R-charge one, generalizing previous results for unoriented non-chiral theories.

Abstract We study 4d SCFTs obtained by orientifold projections on necklace quivers with fractional branes. The models obtained by this procedure are 𝒩 = 1 linear quivers with unitary, symplectic and orthogonal gauge groups, bifundamental and tensorial matter. Remarkably, models that are not dual in the unoriented case can have the same central charges and superconformal index after the projection. The reason for this behavior rests upon the ubiquitous presence of adjoint fields with R-charge one. We claim that the presence of such fields is at the origin of the notion of inherited S-duality on the models’ conformal manifold.

We study 3d N=2 SQCD with symplectic and orthogonal gauge groups and adjoint matter. For USp(2n) with two fundamentals and SO(N) with one vector these models have been recently shown to s-confine. Here we corroborate the validity of this proposal by relating it to the confinement of USp(2n) with four fundamentals and an antisymmetric tensor, using exact mathematical results coming from the analysis of the partition function on the squashed three-sphere. Our analysis allows us to conjecture new s-confining theories for a higher number of fundamentals and vectors, in presence of linear monopole superpotentials. We then prove the new dualities through a chain of adjoint deconfinements and s-confining dualities.

Abstract We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.

We systematically study 3d N=2 dualities for U(Nc) gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by adding an opportune CS contact term for the baryonic symmetry. This allows us to follow the various steps on the three sphere partition function, obtaining exact identities among the new dual phases proposed here. We apply the procedure to various cases, namely SQCD without and with adjoint, chiral dualities and some sporadic cases arising from the real mass flow of models with an E7×U(1) enhancement of the global symmetry.

We classify the global one-form symmetries for non-Lagrangian $\mathcal{N}=3$ SCFTs that arise by the action of $S$-fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of $(p, q)$-strings in the brane setup. The charge lattice of lines is then obtained by finding the ones that are genuine modulo screening by dynamical particles. The one-form symmetries are then extracted from the maximal sub-lattices of mutually local lines. We further comment on the existence of non-invertible symmetries for some of these $\mathcal{N}=3$ SCFTs.