Solving Lauricella String Scattering Amplitudes through Recurrence Relations

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously.Comment: 19 pages. v2: Fig.1 adde

String Scattering Amplitudes and Deformed Cubic String Field Theory

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.Comment: 12 pages, 2 figures, references adde

The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes

We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10].Comment: 19 pages, no figure. v2: 20 pages, typos corrected and Eqs. added. v3: 24 pages, Examples in sec. II added,"Discussion" added, to be published in Nucl.Phys.

Cochlea-sparing acoustic neuroma treatment with 4π radiation therapy.

PurposeThis study investigates whether 4π noncoplanar radiation therapy can spare the cochleae and consequently potentially improve hearing preservation in patients with acoustic neuroma who are treated with radiation therapy.Methods and materialsClinical radiation therapy plans for 30 patients with acoustic neuroma were included (14 stereotactic radiation surgery [SRS], 6 stereotactic radiation therapy [SRT], and 10 intensity modulated radiation therapy [IMRT]). The 4π plans were created for each patient with 20 optimal beams selected using a greedy column generation method and subsequently recalculated in Eclipse for comparison. Organ-at-risk (OAR) doses, homogeneity index, conformity, and tumor control probability (TCP) were compared. Normal tissue complication probability (NTCP) was calculated for sensorineural hearing loss (SNHL) at 3 and 5 years posttreatment. The dose for each plan was then escalated to achieve 99.5% TCP.Results4π significantly reduced the mean dose to both cochleae by 2.0 Gy (32%) for SRS, 3.2 Gy (29%) for SRT, and 10.0 Gy (32%) for IMRT. The maximum dose to both cochleae was also reduced with 4π by 1.6 Gy (20%), 2.2 Gy (15%), and 7.1 Gy (18%) for SRS, SRT, and IMRT plans, respectively. The reductions in mean/maximum brainstem dose with 4π were also statistically significant. Mean doses to other OARs were reduced by 19% to 56% on average. 4π plans had a similar CN and TCP, with a significantly higher average homogeneity index (0.93 vs 0.92) and significantly lower average NTCP for SNHL at both 3 years (30.8% vs 40.8%) and 5 years (43.3% vs 61.7%). An average dose escalation of approximately 116% of the prescription dose achieved 99.5% TCP, which resulted in 32.6% and 43.4% NTCP for SNHL at 3 years and 46.4% and 64.7% at 5 years for 4π and clinical plans, respectively.ConclusionsCompared with clinical planning methods, optimized 4π radiation therapy enables statistically significant sparing of the cochleae in acoustic neuroma treatment as well as lowering of other OAR doses, potentially reducing the risk of hearing loss

Influence of Correlated Disorder Potentials on the Levitation of Current Carrying States in the Quantum Hall Effect

The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice system. We consider a Gaussian correlated random potential, study the behaviour of the current carrying states and trace their energetical position when the disorder strength is increased. Our results qualitatively resemble those obtained previously for exponentially correlated disorder potentials. We find both the downward movement of the anti-Chern states as well as the floating up of the Chern states across the Landau gap which is sometimes masked by the global broadening of the tight binding band.Comment: 4 pages, 3 figures, EP2DS-14 Pragu

Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping

We study the electronic instabilities of near 1/4 electron doped graphene using the functional renormalization group (FRG) and variational Monte-Carlo method. A modified FRG implementation is utilized to improve the treatment of the von Hove singularity. At 1/4 doping the system is a chiral spin density wave state exhibiting the anomalous quantized Hall effect, or equivalently a Chern insulator. When the doping deviates from 1/4, the $d_{x^2-y^2}+i d_{xy}$ Cooper pairing becomes the leading instability. Our results suggest near 1/4 electron or hole doped graphene is a fertile playground for the search of Chern insulators and superconductors.Comment: 7 pages, 8 figures, with technical details, published versio

The SL(K+3,C)SL(K+3,\mathbb{C}) symmetry of string scatterings from D-branes

By using the solvability of Lauricella function $F_{D}^{(K)}\left( \alpha;\beta_{1},...,\beta_{K};\gamma;x_{1},...,x_{K}\right)$ with nonpositive integer $\beta_{J}$, we show that each scattering or decay process of string and D-brane states at \textit{arbitrary} mass levels can be expressed in terms of a single Lauricella function. This result extends the previous exact $SL(K+3,\mathbb{C})$ symmetry of tree-level open bosonic string theory to include the D-brane.Comment: 15 pages, no figure. arXiv admin note: text overlap with arXiv:2108.06326. v2: 18 pages. Final in Nucl.Phys.

Stringy scaling of n-point Regge string scattering amplitudes

We discover a stringy scaling behavior for a class of n-point Regge string scattering amplitudes (RSSA). The number of independent kinematics variables is found to be reduced by dim M.Comment: 33 pages, 1 figur