On Marginal Operators in Boundary Conformal **Field** **Theory**

**field**

**theory**allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension $\Delta$ equal to the space-time dimension $d$ of the conformal

**field**theory, while with a boundary, as long as the operator dimension is protected, one can make up for the difference $d-\Delta$ by including a factor $z^{\Delta-d}$ in the deformation where $z$ is the distance from the boundary. This coordinate dependence does not lead to a reduction in the underlying $SO(d,1)$ global conformal symmetry group of the boundary conformal

**field**

**theory**. We show that such terms can arise from boundary flows in interacting

**field**

**theories**. Ultimately, we would like to be able to characterize what types of boundary conformal

**field**

**theories**live on the orbits of such deformations. As a first step, we consider a free scalar with a conformally invariant mass term $z^{-2} \phi^2$, and a fermion with a similar mass. We find a connection to double trace deformations in the AdS/CFT literature.

10/10 relevant

arXiv

Thermo Field Dynamics Extension of Group **Field** **Theory**

**field**

**theories**are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermo

**field**dynamics extension of group

**field**

**theories**. The starting point is the equilibrium Gibbs states in group

**field**

**theory**recently found by Kotecha and Oriti, based on which we construct the thermo

**field**double state as a "thermal" vacuum respecting the Kubo-Martin-Schwinger condition. We work with the Weyl $C^*$-algebra of group fields, where the group

**fields**and their Hermitian conjuations respectively annihilate and create quantum polyhedra in the sense of second quantization. The thermo

**field**double states are then obtained from the squeezed states on this Weyl algebra. In particular, the "tilde" system is obtained from the original system via modular conjugations, and we interptret the "tilde" system as an emergent referencial system. The thermo

**field**double states, when viewed as states on the group

**field**

**theory**Fock vacuum, are condensate states at finite flow parameter $\beta$. We suggest that the equilibrium flow parameters $\beta$ of the thermo

**field**double states in the group

**field**

**theory**condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.

10/10 relevant

arXiv

Semisimple 4-dimensional topological **field** **theories** cannot detect exotic
smooth structure

**field**

**theories**lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth 4-manifolds and homotopy equivalent simply connected closed oriented smooth 4-manifolds. We show that all currently known 4-dimensional

**field**

**theories**are semisimple, including unitary

**field**theories, and once-extended

**field**

**theories**which assign algebras or linear categories to 2-manifolds. As an application, we compute the value of a semisimple

**field**

**theory**on a simply connected closed oriented 4-manifold in terms of its Euler characteristic and signature. Moreover, we show that a semisimple 4-dimensional

**field**

**theory**is invariant under $\mathbb{C}P^2$-stable diffeomorphisms if and only if the Gluck twist acts trivially. This may be interpreted as the absence of fermions amongst the `point particles' of the

**field**

**theory**. Such fermion-free

**field**

**theories**cannot distinguish homotopy equivalent 4-manifolds. Throughout, we illustrate our results with the Crane-Yetter-Kauffman

**field**

**theory**associated to a ribbon fusion category. As an algebraic corollary of our results applied to this

**field**theory, we show that a ribbon fusion category contains a fermionic object if and only if its Gauss sums vanish.

10/10 relevant

arXiv

Hamiltonian anomalies from extended **field** **theories**

**field**

**theories**as relative field theories, namely field theories taking value in a field

**theory**in one dimension higher, the anomaly field theory. Expand abstract.

**field**

**theories**as relative

**field**theories, namely

**field**

**theories**taking value in a

**field**

**theory**in one dimension higher, the anomaly

**field**

**theory**. We show that when the anomaly

**field**

**theory**is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the state space, or that the latter is really an abelian gerbe rather than an ordinary Hilbert space. We include in the discussion the case of non-invertible anomaly

**field**theories, which is relevant to six-dimensional (2,0) superconformal

**theories**. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous

**theory**. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms, as extended

**field**

**theories**down to codimension 2.

10/10 relevant

arXiv

A new strategy to microscopic modelling of topological entanglement in polymers based on **field** **theory**

**field**

**theory**, the original topological constraints imposed on the fluctuating paths of the polymers become constraints over the configurations of the topological

**fields**that mediate the interactions of topological origin between the monomers. Expand abstract.

**field**

**theory**that describes the statistical behavior of knotted and linked polymer rings following a straightforward algorithm. The treatment is not limited to the partition function of the system, but it allows also to express the expectation values of general observables as

**field**

**theory**amplitudes. Our strategy is illustrated taking as examples the Gauss linking number and a topological invariant belonging to a class of invariants due to Massey. The consistency of the new method developed here is checked by reproducing a previous

**field**theoretical model of two linked polymer rings. After the passage to

**field**theory, the original topological constraints imposed on the fluctuating paths of the polymers become constraints over the configurations of the topological

**fields**that mediate the interactions of topological origin between the monomers. These constraints involve quantities like the cross-helicity which are of interest in other disciplines, like for instance in modeling the solar magnetic

**field**. While the calculation of the vacuum expectation values of generic observables remains still challenging due to the complexity of the problem of topological entanglement in polymer systems, we succeed here to reduce the evaluation of the moments of the Gauss linking number for two linked polymer rings to the computation of the amplitudes of a free

**field**

**theory**.

10/10 relevant

arXiv

General **field** **theory** and weak Euler-Lagrange equation for classical
particle-field systems in plasma physics

**field**

**theory**, the distinguish feature of a classical particle-field system is that the particles and

**fields**reside on different manifolds. Expand abstract.

**field**

**theory**for classical particle-

**field**systems is developed. Compared with the standard classical

**field**theory, the distinguish feature of a classical particle-

**field**system is that the particles and

**fields**reside on different manifolds. The

**fields**are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Especially, the non-vanishing Euler derivative in the weak Euler-Lagrangian equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general

**field**

**theory**. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

10/10 relevant

arXiv

Vacuum energy in the effective **field** **theory** of general relativity II:
Inclusion of fermions and a comment on the QCD contribution

**field**

**theory**of scalar and vector

**fields**interacting with the metric field we have shown that for the cosmological constant term which is fixed by the condition of vanishing vacuum energy the graviton remains massless and there... Expand abstract.

**field**

**theory**of scalar and vector

**fields**interacting with the metric

**field**we have shown that for the cosmological constant term which is fixed by the condition of vanishing vacuum energy the graviton remains massless and there exists a self-consistent effective

**field**

**theory**of general relativity defined on a flat Minkowski background. In the current paper we extend the two-loop analysis for an effective

**field**

**theory**of fermions interacting with the gravitational

**field**and obtain an analogous result. We also address the issues of fine tuning of the strong interaction contribution to the vacuum energy and the compatibility of chiral symmetry in the light quark sector with the consistency of the effective

**field**

**theory**of general relativity in a flat Minkowski background.

10/10 relevant

arXiv

Classical Open String Amplitudes and Boundary String **Field** **Theory**

**field**

**theory**realizes the minimal model of open string

**field**

**theory**. More precisely, we observe that the expansion of the (co)homological vector field, $Q$ of boundary string

**field**

**theory**in the cohomology of its linear part reproduces the S-matrices of perturbative string

**theory**. In mathematical terms, boundary string

**field**

**theory**realizes the minimal model map of the cohomological perturbation lemma.

10/10 relevant

arXiv

Extracting the **field** **theory** description of a quantum many-body system
from experimental data

**field**

**theory**, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology. Expand abstract.

**field**

**theory**is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum

**field**theoretical descriptions and its parameters purely from experimental data. This is accomplished by extracting the one-particle irreducible (1PI) vertices from which one can construct all observables. To match the capabilities of experimental techniques used in quantum simulation experiments, our approach employs a formulation of quantum

**field**

**theory**based on equal-time correlation functions only. We illustrate our procedure by applying it to the quantum sine-Gordon model in thermal equilibrium. The theoretical foundations are illustrated by estimating the irreducible vertices at equal times both analytically and using numerical simulations. We then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract the full two-point function and the interaction vertex (four-point function) and their variation with momentum, encoding the `running' of the couplings. The measured 1PI vertices are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing fundamental questions in quantum

**field**theory, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology.

10/10 relevant

arXiv

Boundary String Current & Weyl Anomaly in Six-dimensional Conformal
**Field** **Theory**

**field**strength $H$,a string current is induced in a six dimensional boundary conformal

**field**

**theory**. This allows us to determine the gauge

**field**contribution to the Weyl anomaly in six dimensional conformal

**field**

**theory**in a $H$-flux background. For the (2,0) superconformal

**field**

**theory**of $N$ M5-branes, the current has a magnitude proportional to $N^3$ for large $N$. This suggests that the degree of freedoms scales as $N^3$ in the (2,0) superconformal

**theory**of $N$ multiple M5-branes. The prediction we have for the Weyl anomaly is a new criteria that the (2,0)

**theory**should satisfy.

10/10 relevant

arXiv