We attempt to describe the moduli space of boundary states in the SU(2) WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to marginal deformations, our solutions exhibit a $\textit{g}$-function different from that of the background (typically lower). Thus, our method effectively combines features of both marginal and relevant deformations. After partially fixing an SU(2) symmetry of the equations of motion, we find families of solutions parameterized by the coefficient of the marginal field associated with the $\textit{J}$ current, and we identify them as Cardy boundary states with varying angle $\textit{θ}$. However, it turns out that these solutions become inconsistent once the marginal parameter exceeds a certain value, implying that they cover only a part of the moduli space. Finally, we also compare the relation between the marginal parameter and the angle $\textit{θ}$ for different solutions and we find evidence suggesting that this relation is universal for certain classes of solutions.

Czechia

Matěj Kudrna

Marginal deformations of SU(2) $\textit{k}$ WZW model boundary states in open string field theory

In this paper, we employ chiral effective field theory to study the process of electron-positron annihilation into four pions in the low energy region within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">m</mi><mo>.</mo></mrow></msub><mo>≤</mo><mn>0.6</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. The prediction of the cross section is obtained through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> chiral perturbation theory up to the next-to-leading order, which is smaller than the experimental data in the energy region [0.6–0.65] GeV, though the data has only a few points and poor statistics. Then, the resonance chiral theory is applied to include the resonance contribution, with the lightest scalars and vectors written in the effective Lagrangians. A series of relevant decay widths and the masses of the vectors are studied to fix the unknown couplings. The resonance contribution should be one order larger than that of the chiral perturbation theory but still one to two orders smaller than the data. The significant discrepancy urged the new experimental measurements to give more guidance. We also compute the leading order hadronic vacuum polarization contribution from the four pion channels to the anomalous magnetic moment of the muon, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>μ</mi></msub></math>. In the energy range from threshold up to 0.6 GeV within resonance chiral theory, the contributions are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.680</mn><mo>±</mo><mn>0.062</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.597</mn><mo>±</mo><mn>0.058</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup></math> for the processes of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, respectively.

China

Jia-Yu Zhou

Hao-Xiang Pan

Ling-Yun Dai

Study of electron-positron annihilation into four pions within chiral effective field theory in the low energy region

We revisit the Holographic duality between SU($\textit{N}$) Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large $\textit{N}$ saddles for correlation functions of Wilson lines in antisymmetric powers Λ ℂ of the fundamental representation. The mathematical structures which appear in the calculation match in detail the data of dual A-model D-branes.

Canada

Davide Gaiotto

Suriyah Rajalingam Kannagi

Sergio Sanjurjo

D-branes and the planar limit of Chern-Simons theory. Link invariants

We generalize chiral perturbation theory with spinless matter fields in the fundamental representation of SU($\textit{N}$) to curved spacetime in the presence of an external gravitational field. This work is motivated by recent interest in investigating energy-momentum tensor matrix elements of matter fields. The complete chiral Lagrangian is constructed, including both minimal extensions from flat spacetime and new curvature-induced terms, up to the next-to-next-to-leading order in the chiral expansion, $$ \mathcal{O}\left({p}^3\right) $$ . We perform a systematic one-loop renormalization of the generating functional using the background field method combined with the heat-kernel technique, and explicitly compute the resulting ultraviolet divergences.

Cheng-Cheng Li

Xiong-Hui Cao

Feng-Kun Guo

Renormalization of chiral perturbation theory with spinless matter field in curved spacetime

We present a high-precision study of the topological susceptibility in SU(3) pure gauge theory in four space-time dimensions. The result is based on ensembles at seven lattice spacings and in seven physical volumes to facilitate a controlled continuum and infinite-volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support the idea that both strategies yield a universal continuum limit; we find <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>top</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0.4775</mn><mo stretchy="false">(</mo><mn>14</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>11</mn><mo stretchy="false">)</mo></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mi>top</mi><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><mo>=</mo><mn>198.1</mn><mo stretchy="false">(</mo><mn>0.7</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2.7</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our Appendix data suggest that the excess kurtosis <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>4</mn></msup><mo stretchy="false">⟩</mo><mo>/</mo><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>2</mn></msup><msup><mo stretchy="false">⟩</mo><mn>2</mn></msup><mo>−</mo><mn>3</mn></math> decreases <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∝</mo><msup><mi>L</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> for large box sizes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>.

Germany

Stephan Dürr

Gianluca Fuwa

Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory

The study of periodic orbits in extreme-mass-ratio inspirals is essential for understanding the dynamics of small bodies orbiting supermassive black holes. In this paper, we study the periodic orbits and their corresponding gravitational wave emissions within the framework of an effective field theory-based extension of general relativity (EFTGR), which incorporates higher-order curvature terms into the Einstein–Hilbert action. We start with a brief analysis of the modified black hole spacetime in EFTGR and examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. Focusing on the impact of the higher-order curvature terms in EFTGR, we examine the properties of periodic orbits, which are characterized by three topological integers ($\textit{z}$, $\textit{w}$, $\textit{v}$) that uniquely classify their trajectories. By analyzing these orbits within EFTGR, we aim to provide new insights into how strong-field deviations from general relativity may manifest in observable phenomena. We then calculate the gravitational waveforms generated by these periodic orbits, identifying potential observational signatures. Our analysis reveals a direct connection between the zoom-whirl orbital behavior of the small compact object and the gravitational waveforms it emits: higher zoom numbers lead to increasingly intricate waveform substructures. The results contribute to a clearer understanding of the dynamical features of EFTGR and open new avenues for probing black hole properties via gravitational wave detection.

Shuo Lu

Hao-Jie Lin

Tao Zhu

Yu-Xiao Liu

Xin Zhang

Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity

Some aspects of two General Relativistic cosmological solutions, an exact $$\Lambda $$ CDM-like cosmological solution $$j=1$$ ($\textit{j}$ is cosmographic jerk parameter), and a specifically designed toy cosmological solution $$j=1+3\varepsilon (q-1/2)$$ ($\textit{q}$ is cosmographic deceleration parameter, $$0<|\varepsilon |<1$$ ) that is capable of accommodating a phantom crossing scenario as suggested by DESI DR2, are studied within the context of $\textit{f}$($\textit{R}$) gravity, by portraying them as a $\textit{flow}$ in the 2-dimensional $\textit{theory space}$ spanned by the quantities $$r=\frac{R f'}{f}, m=\frac{R f''}{f'}$$ . For the $\textit{f}$($\textit{R}$) theories exactly reproducing a background $$\Lambda $$ CDM-like expansion history $$j=1$$ , it is shown by means of a $\textit{cosmographic}$ reconstruction approach that the curvature degree of freedom need not necessarily behave like an effective cosmological constant, and that cosmologies under different possible such theories lead to different possible values of $$\Omega _{m0}$$ . With the theory space analysis, it is also shown that $$\Lambda $$ CDM-mimicking $\textit{f}$($\textit{R}$) cosmologies that asymptote to General Relativistic $$\Lambda $$ CDM in the limit $$q\rightarrow 1/2$$ , are prone to instability under small homogeneous and isotropic perturbation, casting a doubt on achieving an exact $$\Lambda $$ CDM-like cosmological solution $$j=1$$ within $\textit{f}$($\textit{R}$) gravity. Regarding the toy cosmological solution $$j=1+3\varepsilon (q-1/2)$$ that is capable of accommodating a phantom crossing scenario, it is shown that possible underlying $\textit{f}$($\textit{R}$) theories that admit it as a solution are inevitably plagued by tachyonic instability ( $$f''(R)<0$$ ). All the above physically interesting conclusions are derived without explicitly reconstructing, even numerically, the functional form of the underlying $\textit{f}$($\textit{R}$), which demonstrates the edge of the $\textit{r}$-$\textit{m}$ theory space analysis over the traditional explicit reconstruction approach. The methodology is general and can be extended straightforwardly to modified teleparallel or modified symmetric teleparallel gravity.

Thailand

Saikat Chakraborty

Piyabut Burikham

Theory space and stability analysis of General Relativistic cosmological solutions in modified gravity

In Fick’s time-honored theory of diffusion, the system responds instantaneously to external perturbations, resulting in acausal behavior. Maxwell-Cattaneo theory addresses this issue by introducing a relaxation time, rendering the diffusion process causal. We focus on systems where this relaxation time is comparable to the diffusion time and significantly larger than the relaxation times of all other non-conserved operators. In such systems, late-time diffusion is influenced by this relaxation process, leading to a theory of quasi-diffusion. Using the Schwinger-Keldysh Effective Field Theory (SK-EFT) framework, we compare the theories of diffusion and quasi-diffusion by analyzing the real-time dynamics of correlation functions both in linear response and at one-loop order. In particular, we show that the one-loop corrections in the causal (quasi-diffusion) theory, in both the underdamped and the overdamped cases, are governed by two universal functions. In the overdamped case, the behavior mirrors that of the acausal (diffusion) theory, which has recently been applied for precision tests of SK-EFT in diffusive systems. We suggest that our results in the underdamped limit can also be used for precision tests in quasi-diffusive systems.

Navid Abbasi

United States

Matthias Kaminski

Dirk Rischke

Comparison between causal and acausal diffusion: a Schwinger-Keldysh effective field theory perspective

The quantum induced stress tensor of 3+1-dimensional Einstein gravity, with conformally coupled matter, is studied in an effective field theory approach. In this context, Riegert’s non-local effective action is sufficient to reproduce the trace anomaly in curved spacetime but in general the effective action can include additional non-local but scale invariant terms that influence the semiclassical physics without affecting the trace anomaly. Here, a truncated model, with only one additional term involving the square of the Weyl tensor, is used to find the induced stress tensor in a black hole background. With suitable physical conditions, a solution of the resulting 4th order equations leads, in a static limit, to a unique quantum state matching expected properties of the Unruh state.

Bing-Nan Liu

David Lowe

Iceland

Larus Thorlacius

Generalized effective field theory for four-dimensional black hole evaporation

In this work, we study the renormalization-group evolution of parameters in the three-dimensional effective field theory (3D EFT) that describes the thermally driven electroweak phase transition of the Higgs field. We consider tree-level and radiatively generated barriers induced by beyond the Standard Model physics, enabling a first-order phase transition at and below the soft scale, respectively. For each case, we compute the two-loop running of the 3D EFT couplings, including the effects of the leading nonrenormalizable terms. We then analyze how the new contributions to the beta functions compare with those in the super-renormalizable case, highlighting their impact on perturbative computations of the scalar potential, which describes the vacuum structure of the theory. By incorporating higher-order corrections in the mass parameter evolution, as well as the running of other effective operators, we set the stage for testing their impact on phase transition dynamics in lattice simulations.