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Anirban Basu

Publications and source records attributed to Anirban Basu.

At least 19 recordsLinked to original sources
arXiv2023

Algebraic identities between families of (elliptic) modular graphs

Consider an algebraic identity between elliptic modular graphs where several vertices are at fixed locations (and hence unintegrated) while the others are integrated over the toroidal worldsheet. At any unintegrated vertex, we can glue an arbitrary expression involving elliptic modular graphs which has the same unintegrated vertex. Integrating over that vertex, we obtain new algebraic identities between elliptic modular graphs. Hence this elementary process of convoluting the original "seed" identity with other graphs yields infinite number of new identities. We consider various seed identities in which two of the vertices are unintegrated. Convoluting them with families of elliptic modular graphs, we obtain new identities. Each identity is parametrized by an arbitrary number of links in the graphs as well as the positions of unintegrated vertices. On identifying the unintegrated vertices, this leads to an algebraic identity involving modular graphs where all the vertices are integrated over the worldsheet.

hep-th↗
arXiv2023

The price elasticity of Gleevec in patients with Chronic Myeloid Leukemia enrolled in Medicare Part D: Evidence from a regression discontinuity design

Objective To assess the price elasticity of branded imatinib in chronic myeloid leukemia (CML) patients on Medicare Part D to determine if high out-of-pocket payments (OOP) are driving the substantial levels of non-adherence observed in this population. Data sources and study setting We use data from the TriNetX Diamond Network (TDN) United States database for the period from first availability in 2011 through the end of patent exclusivity following the introduction of generic imatinib in early 2016. Study design We implement a fuzzy regression discontinuity design to separately estimate the effect of Medicare Part D enrollment at age 65 on adherence and OOP in newly-diagnosed CML patients initiating branded imatinib. The corresponding price elasticity of demand (PED) is estimated and results are assessed across a variety of specifications and robustness checks. Data collection/extraction methods Data from eligible patients following the application of inclusion and exclusion criteria were analyzed. Principal findings Our analysis suggests that there is a significant increase in initial OOP of $232 (95% Confidence interval (CI): $102 to $362) for individuals that enrolled in Part D due to expanded eligibility at age 65. The relatively smaller and non-significant decrease in adherence of only 6 percentage points (95% CI: -0.21 to 0.08) led to a PED of -0.02 (95% CI: -0.056, 0.015). Conclusion This study provides evidence regarding the financial impact of coinsurance-based benefit designs on Medicare-age patients with CML initiating branded imatinib. Results indicate that factors besides high OOP are driving the substantial non-adherence observed in this population and add to the growing literature on PED for specialty drugs.

econ.EM↗
arXiv2021

Worldsheet (anti)instanton bound states in type II on $T^2$

The 1/8 BPS $D^6\mathcal{R}^4$ coupling in type II string theory compactified on $T^2$ receives contributions from worldsheet instantons and anti-instantons wrapping the $T^2$, up to genus three in string perturbation theory. These involve contributions separately from bound states of instantons and anti-instantons, which are qualitatively similar to such contributions to the 1/2 and 1/4 BPS couplings. At genus two, the $D^6\mathcal{R}^4$ coupling also receives contributions from instanton/anti-instanton bound states unlike the 1/2 and 1/4 BPS couplings, which is a consequence of a T-duality invariant eigenvalue equation a term in the coupling satisfies. We solve this eigenvalue equation to obtain the complete structure of the worldsheet (anti)instanton contributions. In the type IIB theory, strong weak coupling duality leads to certain contributions involving bound states of D string (anti)instantons wrapping the $T^2$.

hep-th↗
arXiv2021

Poisson equation for genus two string invariants: a conjecture

We consider some string invariants at genus two that appear in the analysis of the $D^8\mathcal{R}^4$ and $D^6\mathcal{R}^5$ interactions in type II string theory. We conjecture a Poisson equation involving them and the Kawazumi--Zhang invariant based on their asymptotic expansions around the non--separating node in the moduli space of genus two Riemann surfaces.

hep-th↗
arXiv2021

Integrating simple genus two string invariants over moduli space

We consider an Sp(4,Z) invariant expression involving two factors of the Kawazumi--Zhang (KZ) invariant each of which is a modular graph with one link, and four derivatives on the moduli space of genus two Riemann surfaces. Manipulating it, we show that the integral over moduli space of a linear combination of a modular graph with two links and the square of the KZ invariant reduces to a boundary integral. We also consider an Sp(4,Z) invariant expression involving three factors of the KZ invariant and six derivatives on moduli space, from which we deduce that the integral over moduli space of a modular graph with three links reduces to a boundary integral. In both cases, the boundary term is completely determined by the KZ invariant. We show that both the integrals vanish.

hep-th↗
arXiv2021

Relations between elliptic modular graphs

We consider certain elliptic modular graph functions that arise in the asymptotic expansion around the non--separating node of genus two string invariants that appear in the integrand of the $D^8 R^4$ interaction in the low momentum expansion of the four graviton amplitude in type II superstring theory. These elliptic modular graphs have links given by the Green function, as well its holomorphic and anti--holomorphic derivatives. Using appropriate auxiliary graphs at various intermediate stages of the analysis, we show that each graph can be expressed solely in terms of graphs with links given only by the Green function and not its derivatives. This results in a reduction in the number of basis elements in the space of elliptic modular graphs.

hep-th↗
arXiv2020

Zero mode of the Fourier series of some modular graphs from Poincare series

We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with $2s$ links for $s=2, 3$ and $4$. In each case, it satisfies an eigenvalue equation with source terms involving $E_{2s}$ and $E_s^2$ only. On removing certain combinations of $E_{2s}$ and $E_s^2$ from it, we express the resulting expression as an absolutely convergent Poincare series. This is used to calculate the power behaved terms in the asymptotic expansion of the zero mode of the Fourier expansion of these graphs in a simple manner.

hep-th↗
arXiv2019

Transcendentality violation in type IIB string amplitudes

We analyze transcendentality for certain terms that arise in multiloop amplitudes in the low momentum expansion of the four graviton amplitude in type IIB string theory in ten dimensions, based on the constraints of supersymmetry and S--duality. This leads to several contributions that violate transcendentality beyond one loop at all orders in the low momentum expansion. We also perform a similar analysis for the five graviton amplitude, obtaining contributions that involve single--valued multiple zeta values beyond tree level.

hep-th↗
arXiv2019

Eigenvalue equation for the modular graph $C_{a,b,c,d}$

The modular graph $C_{a,b,c,d}$ on the torus is a three loop planar graph in which two of the vertices have coordination number four, while the others have coordination number two. We obtain an eigenvalue equation satisfied by $C_{a,b,c,d}$ for generic values of $a,b,c$ and $d$, where the source terms involve various modular graphs. This is obtained by varying the graph with respect to the Beltrami differential on the toroidal worldsheet. Use of several auxiliary graphs at various intermediate stages of the analysis is crucial in obtaining the equation. In fact, the eigenfunction is not simply $C_{a,b,c,d}$ but involves subtracting from it specific sums of squares of non--holomorphic Eisenstein series characterized by $a,b,c$ and $d$.

hep-th↗
arXiv2019

Eigenvalue equation for genus two modular graphs

We obtain a second order differential equation on moduli space satisfied by certain modular graph functions at genus two, each of which has two links. This eigenvalue equation is obtained by analyzing the variations of these graphs under the variation of the Beltrami differentials. This equation involves seven distinct graphs, three of which appear in the integrand of the $D^8\mathcal{R}^4$ term in the low momentum expansion of the four graviton amplitude at genus two in type II string theory.

hep-th↗
arXiv2018

Supergravity limit of genus two modular graph functions in the worldline formalism

We consider the contributions upto the $D^{10} \mathcal{R}^4$ terms in the low momentum expansion of the two loop four graviton amplitude in maximal supergravity that arise in the field theory limit of genus two modular graph functions that result from the low momentum expansion of the four graviton amplitude in toroidally compactified type II string theory, using the worldline formalism of the first quantized superparticle. The expression for the two loop supergravity amplitude in the worldline formalism allows us to obtain contributions from the individual graphs, unlike the expression for the same amplitude obtained using unitarity cuts which only gives the total contribution from the sum of all the graphs. Our two loop analysis is field theoretic, and does not make explicit use of the genus two string amplitude.

hep-th↗
arXiv2017

A simplifying feature of the heterotic one loop four graviton amplitude

We show that the weight four modular graph functions that contribute to the integrand of the t_8 t_8 D^4 R^4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the graphs that contribute to the integrands of the other gravitational terms at this order in the low momentum expansion, and these integrands require regularization. This property persists for an infinite number of terms in the effective action, and their integrands do not require regularization. We find non--trivial relations between weight four graphs of distinct topologies that do not require regularization by performing trivial manipulations using auxiliary diagrams.

hep-th↗
arXiv2017

Low momentum expansion of one loop amplitudes in heterotic string theory

We consider the low momentum expansion of the four graviton and the two graviton--two gluon amplitudes in heterotic string theory at one loop in ten dimensions, and analyze contributions upto the D^2 R^4 interaction from the four graviton amplitude, and the D^4 R^2 F^2 interaction from the two graviton--two gluon amplitude. The calculations are performed by obtaining equations for the relevant modular graph functions that arise in the modular invariant integrals, and involve amalgamating techniques used in the type II theory and the calculation of the elliptic genus in the heterotic theory.

hep-th↗
arXiv2017

Simplifying the one loop five graviton amplitude in type IIB string theory

We consider the D^8 R^5 and D^{10} R^5 terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of SL(2,Z). Unlike the graphs which arise in the four graviton amplitude or at lower orders in the momentum expansion of the five graviton amplitude where the links are given by scalar Green functions, there are several graphs for the D^8 R^5 and D^{10} R^5 terms where two of the links are each given by a derivative of the Green function. Starting with appropriate auxiliary diagrams, we show that these graphs can be expressed in terms of those which do not involve any derivatives. This results in considerable simplification of the amplitude.

hep-th↗
arXiv2016

Proving relations between modular graph functions

We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non--trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links.

hep-th↗
arXiv2016

Poisson equation for the three loop ladder diagram in string theory at genus one

The three loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D^{12} R^4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one, two and three loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.

hep-th↗